Multi-modal dynamic variational autoencoders for longitudinal analysis of multi-omics data

Abstract

Systems and methods are provided for creating and training a model for determining a clinical outcome from multi-omics data collected longitudinally. A training dataset is created for a patient. A differentiable Kalman filter module is created for modeling the latent dynamics of input multi-omics data. A second inverse compositional transform module is created for creating filtered multi-omics data from latent representations of the multi-omics data. A third encoder neural network module is created that encodes the matrix data, producing compressed data. A fourth decoder neural network module is created for reconstructing the compressed data, producing original input data. A fifth automatic differentiation module is created that integrates the first, third, and fourth modules into DVAE model. The model is trained using a subset of the training dataset, hyper-parameter tuning is applied using another subset of the training dataset, and the model accuracy is evaluated on a holdout dataset.

Description

MULTI-MODAL DYNAMIC VARIATIONAL AUTOENCODERS FOR LONGITUDINAL ANALYSIS OF MULTI-OMICS DATA RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application Serial No.63 / 510,948, filed on June 29, 2023, the content of which is incorporated by reference herein in its entirety. FIELD

[0002] The teachings herein relate to systems and methods for building an artificial intelligence (AI) or machine learning (ML) model for analyzing a plurality of multi-omics data for a patient to determine a clinical outcome. INTRODUCTION

[0003] Identifying appropriate clinical interventions for patients is challenging due to the biological heterogeneity underlying patients. For example, the efficacy of immunotherapy treatments is approximately 30%, highlighting that most cancer patients are not able undergo remission after treatment. Despite the promise of these therapies, the ability to predict patient response remains elusive, particularly in the context of fecal microbiota transplantation (FMT), where no established predictive models exist.

[0004] In the field of multi-omics data integration and precision medicine, several products and methodologies exist that attempt to address the same problem of understanding biological systems and identifying molecular signatures associated with different clinical treatments and different conditions. However, these existing products and methodologies have certain limitations.

[0005] Some methodologies, such as mixOmics and multi-omics facto analysis (MOFA), focus on statistical methodologies like canonical correlation analysis (CCA) and partial leastsquares (PLS) for integrating multi-omics data. These methods aim to learn common latent factors and identify biomarkers but fall short in handling large datasets with high sparsity or incorporating the compositional nature of the data. Deep learning frameworks like scVI and MOVE employ non-linear dimensionality reduction using variational autoencoders (VAEs). While they synchronize omics layers, they may not fully address the challenges of integrating diverse omics platforms or accounting for missing data and experimental designs. Methods like MMvec tackle the challenge of compositional data and estimating co-occurrence probabilities between microbes and metabolites but cannot incorporate absolute quantification, a key quality required for inferring differential abundance of biomarkers (i.e. microbes, metabolites, transcripts, proteins, viruses, etc). Moreover, existing methodologies often assume complete data and struggle to handle missing data, and there is a need for linking multi-omics integration methods in observational cohorts and clinical trials.

[0006] In addition to the aforementioned limitations, an important challenge that the existing methodologies face is their inability to handle batch effects, which arise from differences in protocols and laboratory conditions across multiple studies. This limitation has a significant impact on their scalability and accuracy. Without the ability to address batch effects, these methods are constrained in terms of the size of the training dataset that can be effectively used, resulting in limited accuracy of the models. Moreover, the inability to handle batch effects greatly restricts the practical applicability of these computational methods. It hampers their usefulness in designing new experiments, conducting clinical trials, and serving as diagnostics for new patients. Since real-world biological applications involve diverse datasets collected from different sources and settings, the inability to account for batch effects undermines the reliability and generalizability of these methods.

[0007] In summary, while various products and methodologies attempt to solve the problem of multi-omics data integration and precision medicine, they often have limitationsin terms of handling data properties, missing data, compositional nature, and experimental designs. As a result, there is a need for systems and methods that can analyze biomarkers and their causal effects on clinical or experimental outcomes while overcoming challenges related to scalability, high dimensionality, small sample size, missing data, and the ability to handle batch effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The skilled artisan will understand that the drawings, described below, are for illustration purposes only. The drawings are not intended to limit the scope of the present teachings in any way.

[0009] Figure 1 is a block diagram that illustrates a computer system, upon which embodiments of the present teachings may be implemented.

[0010] Figure 2 is an exemplary table showing the advantages of the DVAE model over competing software technologies, in accordance with various embodiments.

[0011] Figure 3 is an exemplary diagram showing the adaptability of the DVAE model, in accordance with various embodiments.

[0012] Figure 4 is an exemplary diagram showing how latent representations within the DVAE model are computed using autoencoding, in accordance with various embodiments.

[0013] Figure 5 is an exemplary series of plots showing dynamic proof-of-concept forecasting multi-omics profiles and patient outcomes, in accordance with various embodiments.

[0014] Figure 6 is an exemplary plot showing a proof-of-concept forecasting patient outcomes using a log-ratio constructed from two sets of microbes identified from the Shapley values generated from the model, in accordance with various embodiments.

[0015] Figure 6A is an exemplary diagram, showing a timeline of a typical FMT study, collecting biological samples x and patient outcomes w before and after the intervention u, in accordance with various embodiments.

[0016] Figure 7 is an exemplary diagram showing the training procedure for the DVAE model, in accordance with various embodiments.

[0017] Figure 8 is an exemplary diagram showing the usage procedure for the DVAE model, in accordance with various embodiments.

[0018] Figure 9 is a flowchart showing a method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, in accordance with various embodiments.

[0019] Figure 10 is a schematic diagram of a system that includes one or more distinct software modules that perform a method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, in accordance with various embodiments.

[0020] Before one or more embodiments of the present teachings are described in detail, one skilled in the art will appreciate that the present teachings are not limited in their application to the details of construction, the arrangements of components, and the arrangement of steps set forth in the following detailed description or illustrated in the drawings. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. DESCRIPTION OF VARIOUS EMBODIMENTS COMPUTER-IMPLEMENTED SYSTEM

[0021] Figure 1 is a block diagram that illustrates a computer system 100, upon which embodiments of the present teachings may be implemented. Computer system 100 includes abus 102 or other communication mechanism for communicating information, and a processor 104 coupled with bus 102 for processing information. Although processor 104 is shown as a single processor in Figure 1, in various embodiments processor 104 can include two or more processors. As a result, processor 104 can be one or more processors. These one or more processors can include, but are not limited to, one or more central processing units (CPUs), one or more graphics processing units (GPUs), one or more neural network processing units (NPUs), or one or more tensor processing units (TPUs). In other words, one or more processors 104 can include any combination of CPUs, GPUs, NPUs, and TPUs.

[0022] Computer system 100 also includes a memory 106, which can be a random-access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing instructions to be executed by processor 104. Memory 106 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 104. Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0023] Computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is cursor control 116, such as a mouse, a trackball or cursor direction keys for communicating direction information and command selections to processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (i.e., x) and a second axis (i.e., y), that allows the device to specify positions in a plane.

[0024] A computer system 100 can perform the present teachings. Consistent with certain implementations of the present teachings, results are provided by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in memory 106. Such instructions may be read into memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in memory 106 causes processor 104 to perform the process described herein. Alternatively hard-wired circuitry may be used in place of or in combination with software instructions to implement the present teachings. Thus, implementations of the present teachings are not limited to any specific combination of hardware circuitry and software.

[0025] In various embodiments, computer system 100 can be connected to one or more other computer systems, like computer system 100, across a network to form a networked system. The network can include a private network or a public network such as the Internet. In the networked system, one or more computer systems can store and serve the data to other computer systems. The one or more computer systems that store and serve the data can be referred to as servers or the cloud, in a cloud computing scenario. The one or more computer systems can include one or more web servers, for example. The other computer systems that send and receive data to and from the servers or the cloud can be referred to as client or cloud devices, for example.

[0026] The term “computer-readable medium” as used herein refers to any media that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 110. Volatile media includes dynamic memory, such as memory 106.Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 102.

[0027] Common forms of computer-readable media or computer program products include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, digital video disc (DVD), a Blu-ray Disc, any other optical medium, a thumb drive, a memory card, a RAM, PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, or any other tangible medium from which a computer can read.

[0028] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on the magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infra-red transmitter to convert the data to an infra-red signal. An infra-red detector coupled to bus 102 can receive the data carried in the infra-red signal and place the data on bus 102. Bus 102 carries the data to memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by memory 106 may optionally be stored on storage device 110 either before or after execution by processor 104.

[0029] In accordance with various embodiments, instructions configured to be executed by a processor to perform a method are stored on a computer-readable medium. The computer-readable medium can be a device that stores digital information. For example, a computer-readable medium includes a compact disc read-only memory (CD-ROM) as is known in the art for storing software. The computer-readable medium is accessed by a processor suitable for executing instructions configured to be executed.

[0030] The following descriptions of various implementations of the present teachings have been presented for purposes of illustration and description. It is not exhaustive and does not limit the present teachings to the precise form disclosed. Modifications and variations are possible in light of the above teachings or may be acquired from practicing of the present teachings. Additionally, the described implementation includes software but the present teachings may be implemented as a combination of hardware and software or in hardware alone. The present teachings may be implemented with both object-oriented and non-object- oriented programming systems. DYNAMIC VARIATIONAL AUTOENCODER

[0031] In accordance with various embodiments, the following terms are used herein as follows.

[0032] Intervention is a method or procedure applied to modify a disease process, condition, or other health-related issue. In clinical research, an intervention refers to a treatment, procedure, or other regimen that is the subject of study. Examples of interventions include immunotherapy treatment, dietary intervention, fecal matter transplant or consumption of drugs including small molecule drugs or antibody drugs.

[0033] Outcome is the result or consequence of an intervention. In clinical trials, outcomes are the measured variables used to determine the effectiveness of an intervention. Examples of outcomes include tumor size, behavioral questionnaires (i.e. Childhood Autism Rating Scale), gastrointestinal symptom questionnaires, or inflammatory measurements (i.e. cytokine concentrations).

[0034] Omics is a field of study in biology ending with -omics, such as genomics, transcriptomics, proteomics, metabolomics that focuses on the collective characterization andquantification of pools of biological molecules that translate into the structure, function, and dynamics of an organism or organisms.

[0035] Multi-omics is an integrative approach that analyzes and interprets data from various omic disciplines, such as genomics, proteomics, and metabolomics, to understand the relationships and interactions within a biological system.

[0036] Confounder is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounders are often controlled for in the design and analysis of experiments. Examples of confounders include patient age, sex, medical history or demographics.

[0037] Variational Autoencoder (VAE) is a type of autoencoder that generates a probabilistic representation of input data. It was originally used for tasks like image generation and denoising.

[0038] Dynamic Variational Autoencoder is an extension of the VAE that models sequential data and captures temporal dynamics, originally used in video or speech analysis.

[0039] Microbiome is the collective genomes of the microbes (composed of bacteria, bacteriophage, fungi, protozoa, and viruses) that live inside and on the human body.

[0040] Metabolomics is the scientific study of chemical processes involving metabolites, the small molecule substrates, intermediates, and products of metabolism.

[0041] Genetics is the study of genes, genetic variation, and heredity in living organisms. It is generally considered a field of biology but intersects frequently with many other life sciences.

[0042] Proteomics is the large-scale study of proteomes, which are sets of proteins produced in an organism, system, or biological context.

[0043] Transcriptomics is the study of the transcriptome—the complete set of RNA transcripts produced by the genome at any one time.

[0044] Hypertune is the process of adjusting the parameters of a model to improve its performance, often using methods like grid search or random search.

[0045] Model fit is a statistical measure that describes how well a model approximates real-world data. Good model fit indicates that the model accurately represents the data.

[0046] Differentiable refers to differentiable mathematical functions that are smooth enough to have a derivative, which can be used in optimization and machine learning algorithms.

[0047] Differentiable Kalman Filter is a variant of the Kalman Filter that can be integrated into neural networks and trained via backpropagation.

[0048] Training dataset is a subset of data used to train models. The model learns to recognize patterns in this data.

[0049] Holdout dataset is a subset of data not used in training the model, used to test the model’s predictive power and prevent overfitting.

[0050] Model accuracy is a measure of a model’s predictive accuracy. Examples include Pearson’s r, which measures linear correlation, and classification accuracy, which measures the percentage of correct predictions in classification tasks.

[0051] Patient metadata is information about patients that can include confounders, clinical outcomes, clinical interventions, and other relevant data used in analysis.

[0052] Inverse Compositional Transform is a mathematical operation that reverses log- ratio transformations, such as the inverse isometric log-ratio (ILR) or inverse centered log- ratio (CLR), to convert data from a log-transformed space back to proportions.

[0053] Immunotherapy is a type of cancer treatment that helps your immune system fight cancer.

[0054] Fecal Matter Transplant (FMT) is a procedure where fecal matter, or stool, is collected from a screened donor and placed into a patient’s gastrointestinal tract to treat certain conditions.

[0055] Longitudinal, as it pertains to data, involves repeated observations of the same variables over an extended period of time, allowing for the study of changes and long-term patterns.

[0056] As described above, there is a need for systems and methods that can analyze biomarkers and their causal effects on clinical or experimental outcomes while overcoming challenges related to scalability, high dimensionality, small sample size, missing data, and the ability to handle batch effects.

[0057] In various embodiments, a dynamic variational autoencoder (DVAE) framework or model offers a range of advantages that enhance its capabilities in analyzing multi-omics data for patient stratification and predicting treatment outcomes. This DVAE model provides effective handling of high-dimensional data, for example. The DVAE model captures high- dimensional dynamics by assuming a low-dimensional “latent” structure, enabling accurate and scalable inference.

[0058] Note that the DVAE model can also be referred to as a DVAE model. This DVAE model is, for example, an artificial intelligence (AI) model or machine learning (ML) model.

[0059] In various embodiments, the DVAE model provides effective handling of multi- modal data. The DVAE model can integrate diverse molecular modalities such as metagenomics, transcriptomics, proteomics, and metabolomics. For example, incorporating microbiome data can improve the prediction of transcriptome abundances in a longitudinal COVID study, enhancing the ability to predict a subject's inflammatory response. Similar benefits can be obtained when predicting treatment responses in clinical trials. Note thatlongitudinal studies or data include data points that are collected over time. In other words, longitudinal data can include time series data.

[0060] In various embodiments, the DVAE model provides analysis of compositional data. The DVAE model effectively analyzes compositional data types, such as sequencing and mass spectrometry data, which only provide relative information. This capability is particularly relevant in metabolomics datasets where concentration information is not available, enabling more accurate inference (absolute quantification with MS is possible, but is rather laborious and can only be practically achieved for a handful of metabolites of interest).

[0061] In various embodiments, the DVAE model provides confounder adjustment. The DVAE model addresses confounding factors in clinical trials, including demographics, age, sex, and batch effects. The DVAE model shows that focusing on within-study differences cancels out batch effects, allowing inferences within-study longitudinal dynamics, which allows aggregation of dynamical information across datasets.

[0062] In various embodiments, the DVAE model provides high statistical power via transfer learning. The DVAE model utilizes transfer learning, leveraging pretraining on diverse cross-sectional studies and different microbial sequencing data types such as 16S and SMS. This approach overcomes the challenge of small sample sizes, boosting the reliability of predictions and expanding the applicability of our models across different patient cohorts and diseases.

[0063] In various embodiments, the DVAE model provides efficient longitudinal analysis. The DVAE model incorporates repeated measurements collected at irregular intervals or varying time points. This enables the exploration of temporal dynamics and the identification of biomarkers associated with disease progression and treatment response.

[0064] In various embodiments, the DVAE model provides improved interpretability. The neural network architecture of the DVAE model, combined with insights from compositional data analysis, allows for the identification of biomarkers predictive of favorable clinical outcomes. This enhances interpretability, providing valuable insights into the underlying biological mechanisms and enabling informed decisions for precision medicine.

[0065] Figure 2 is an exemplary table 200 showing the advantages of the DVAE model over competing software technologies, in accordance with various embodiments. In table 200, the capabilities of DVAE model 210 are compared to existing multi-omics integration methods. In table 200, the symbol (x) is indicative of a property that a method satisfies, and the symbol (?) denotes that there is ambiguity. The list of competing tools is not exhaustive but provides a high-level overview of the state of the field.

[0066] In various embodiments, the DVAE model is able to integrate multiple omics across cohorts and sampling intervals by leveraging VAEs in tandem with a differentiable Kalman Filter. In various embodiments, Kalman Filtering is performed in the lower dimensional latent space, which allows an approximation of high dimensional dynamics. The full model is detailed as follows

[0067] ^^^ ^^௧| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^ ^^௧^^, ^^^ ^^௧| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^௧, ^^^

[0068] ^^^ ^^௧| ^^௧ି^, ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^௧ି^^ ^^௧^^௧^ ^^^, ^^^ ^^^ ^^௧| ^^௧^ ൌ

[0069] where ^^௧represents high dimensional sequencing count measurements (aka microbial abundances across |X| microbial species), ^^௧represents the latent representation of a measurement collected at time t, ^^௧represents the latent state representation at time t, ^^௧represents clinical interventions across | ^^| possible interventions, and ^^^^௧^represents a random intercept for a study k. ^^௧represents the transition matrix between latent states attime point t, ^^௧represents the perturbation at time point t, and ^^௧represents the projection matrix to obtain the measurements ^^௧from the latent state ^^௧. The functions ^^ and ^^ represent the encoder and decoder neural networks from the pre-trained VAEs. Q, R are both pre-specified covariance matrices and D is an estimable diagonal covariance matrix. To fit these models, the Evidence Lower Bound (ELBO) is maximized, which is given as ^^ ^^ ^^ ^^ ൌ ^^^^௫|௭^ ^^௭|^^ ^^^|௨^^^^,௭|௫,௨^^^^௭|௫^ ^^^|௭,௨^^

[0070] The DVAEThe DVAE model has a comparable prediction accuracy to the state-of-the-art on small datasets (r=0.18 on the Mefisto tutorial, but is >100x faster, enabling it to scale to datasets with tens of thousands of dimensions, and multiple studies. Furthermore, by using the Multinomial distribution in addition to compositional transforms baked within the ^^ and ^^ encoder / decoder networks, inference can be performed on highly sparse data while accounting for biases that can arise from analyzing compositional data. Finally, by leveraging the pre-trained VAEs and modeling batch effects, multiple clinical studies can be aggregated together and cross- sectional studies can be leveraged to increase the sample size, closing the dimensionality gap, which is the biggest challenge for competing AI technologies.

[0071] In various embodiments, the DVAE model addresses the challenges of generalizability and interpretability. In order to tackle the generalizability challenge, the DVAE model has been made to be adaptable across different cohorts.

[0072] Figure 3 is an exemplary diagram 300 showing the adaptability of the DVAE model, in accordance with various embodiments. In diagram 300, each of the boxes represents latent representations z from their omics-specific VAE model. These latent quantities are leveraged for the bulk of the complex modeling, including inferring interactions across omics levels, inferring the effect of external interventions such as FMT, and predicting clinical outcomes, while controlling for various confounders. In the case ofmodeling complex interventions such as FMT, the entire donor microbiome and metabolome can be modeled via their latent representations to further constrain the model while enabling the inference of the impact of individual donor microbes and metabolites. Other relevant technologies that can be leveraged for modeling multi-omic interactions include, but are not limited to proteomics, transcriptomics, spatial metabolomics, spatial transcriptomics, qPCR, targeted metabolomics, flow cytometry, electronic healthcare records, fluorescence imaging, histology imagine, tissue imaging, and neuroimaging.

[0073] Within the multi-omics interactions box, boxes containing z variables represents latent representations for a given omics modality at a given timepoint for a given patient. Latent representations at a given time step are directly computed from the interaction of all the latent representations at a previous time step, in addition to interventions applied in the current time step. Multi-omics datasets here represent plasma metabolites, fecal metabolites, peripheral blood mononuclear cells (PBMC) transcriptomics, PBMC proteomics, fecal proteomics and fecal microbes collected for a single patient. Confounders such as age and sex are used to initialize the multi-omics latent representations at the first timepoint for. Outcomes such as behavioral, communication and sleep assessments are directly computed from the multi-omics latent representations.

[0074] In various embodiments, the DVAE model can leverage many different encoder / decoder neural network architectures, such as sparse autoencoders, multi-layer perceptions, convolutional neural networks, transformer, or graph neural network layers, to enhance the generalization capabilities of our models. Given that different clinical cohorts often have largely non-overlapping microbiome compositions, there is biological motivation to leverage sparsity or regularization techniques to better model microbial compositions across largely heterogeneous human populations. Similar challenges are present when dealing with other omics levels such as metabolomics and proteomics, requiring non-standardencoder / decoder architectures. These approaches can help reduce overfitting and improve the transferability of learned features across diverse cohorts.

[0075] Figure 4 is an exemplary diagram 400 showing the pretraining process of the DVAE model, in accordance with various embodiments. Large datasets allow the pre- training of parts of the DVAE model to borrow information from other studies and boost statistical power. This ultimately allows the training of high-quality VAEs to perform dimensionality reduction for each omics level and enables dynamical inference to be performed in the lower dimensional latent space.

[0076] The pretraining process involves inferring a compressed version of the input data. Underneath the hood, this involves a two-stage regression, a regression to infer the latent representation z from the input abundances x via the encoder neural network, and a regression to reconstruct the abundances from the latent representation z via the decoder neural network. This overall process is commonly referred to as autoencoding, and linear versions of this process have been shown to be connected to principal components analysis, where the intermediate latent representations z can be leveraged for downstream modeling. Furthermore, there have been a number of extensions to this framework that have allowed for non-linear dimensionality reduction, Bayesian uncertainty estimation, and dealing with sparse inputs as well as compositional data.

[0077] In various embodiments, the DVAE model can incorporate many different types of confounders such as age, sex, diet, and demographics to improve the robustness and generalizability of our models. This can also not only boost model quality but also enable the DVAE model to generalize to model patient responses from marginalized communities. However, these confounding variables may not be recorded across all of the subjects, thus techniques from semi-supervised learning are used to incorporate these confounding factors when they are available.

[0078] In various embodiments, case studies have demonstrated that the integration of multiple omics levels enhances forecasting accuracy when compared to models based on individual omics levels. Therefore, there is a strong rationale for incorporating a diverse range of omics levels into the training procedure. These models can include, but are not limited to, multiple data modalities such as 16S amplicon sequencing, shotgun metagenomics, metabolomics, proteomics, metatranscriptomics as well as wearables, imaging data, audio data, and electronic healthcare record data.

[0079] In various embodiments, due to the ability to perform pretraining, the DVAE model can also handle high-dimensional interventions. In practice, this enables the modeling of complex interventions such as fecal matter transplants (FMTs), where the intervention involves donor stool containing hundreds of thousands of molecules, proteins, transcripts, microbes, and viruses.

[0080] Figure 5 is an exemplary series of plots 500 showing dynamic proof-of-concept forecasting multi-omics profiles and patient outcomes, in accordance with various embodiments. Scatterplots (a-f) of plots 500 show observed vs predicted abundances using data from an autism FMT study. The DVAE model was trained on 14 children in the cohort and the predictions presented here were on the remaining 4 children in the cohort after the FMT. The high accuracy of the DVAE model is partially due to the ability to leverage 20K samples from curated MetagenomicData to boost statistical power while enabling dynamic modeling in a lower dimensional latent space to reduce modeling complexity. Plots (g-h) provide predicted patient outcomes by using leave-one-donor-out (LODO) cross-validation for Crohn’s disease and Melanoma. The DVAE model predicted remission in Crohn’s disease patients (AUROC=0.7) and tumor remission in melanoma patients after immunotherapy (AUROC=0.85).

[0081] In various embodiments, the DVAE model can handle non-linear, high- dimensional time series data by modeling non-linear dynamics in the lower dimensional space. Examples of neural network architectures that can enable this nonlinear latent modeling include, but are not limited to, Kalman Filters, Sequential Monte Carlo, Gaussian Processes, and Neural ODEs.

[0082] In various embodiments, to make the DVAE model useful for clinical trials, two- stage models are fitted to predict clinical outcomes from longitudinal data. This approach involves fitting classifiers on predictions generated from the DVAE model, providing several benefits. Firstly, two-stage models help mitigate the challenge of irregularly spaced sampling, which commonly poses a problem for most classifiers. By leveraging the predictions from the DVAE model, this issue is effectively addressed and the overall performance of the classifiers is improved. Additionally, these two-stage models enable dimensionality reduction, serving as a feature selection step for downstream classifiers. Examples of second-stage models include but are not limited to: K-nearest-neighbors regression, Elastic-net regression, Ensemble methods (e.g. Random Forests), multiple-layer perceptrons, recurrent neural networks, and hidden Markov models. A key advantage of innovation addresses is the ability to perform prediction of clinical outcomes from a limited set of samples, while simultaneously providing a ranked list of biomarkers for further investigation in developing targeted diagnostics. The scarcity of clinical outcomes (i.e. immunotherapy response information) in the available studies presents a few-shot scenario, requiring specialized methodologies to operate effectively.

[0083] Moreover, the DVAE model not only makes predictions but also offers a ranked list of biomarkers that prioritizes the development of target diagnostics. Each of the proposed methodologies within our framework possesses the capability to generate such a ranked list. Techniques such as extracting log-fold changes from linear models and sorting them, orutilizing feature importances from Shapely values or GradCAM, can identify influential biomarkers. Finally, various embodiments can perform causal inference by incorporating a unique combination of do-calculus and GradCAM techniques, enabling the conditional average treatment effect (CATE) to be estimated and causal relationships between biomarkers and clinical outcomes to be identified. By leveraging interventions guided by instrumental variables, the causal effects of biomarkers on clinical outcomes are discerned. The application of do-calculus, a powerful tool from causal inference, in conjunction with GradCAM enhances the ability to uncover causal relationships in complex biological systems. This allows the CATE to be estimated, providing valuable insights into the impact of biomarkers on clinical outcomes while accounting for confounding factors and potential biases. Furthermore, by employing interventions guided by instrumental variables, causal links between biomarkers and clinical outcomes are established. These instrumental variables act as proxies that enable the challenges associated with confounding variables to be overcome, thereby improving the accuracy and robustness of the causal effect estimation. Through the utilization of these innovative techniques, the field of precision medicine is advanced by providing a reliable and efficient means of identifying and quantifying the causal effects of biomarkers on clinical outcomes. This has far-reaching implications for personalized treatment strategies, clinical decision-making, and the development of targeted interventions for improved patient outcomes.

[0084] In various embodiments, the DVAE model includes one or more of the following steps.

[0085] In a first step, a comprehensive training dataset is curated by assembling subject IDs, time points, confounders, experimental interventions, and experimental outcome information. This dataset is linked to corresponding multi-omics datasets, such as sequencing datasets, mass spectrometry datasets, image processing datasets, or text documents.

[0086] In a second step, a differentiable Kalman Filter is developed that is able to perform forecasting from input data. This module is required to be capable of computing the evidence lower bound (ELBO) and its gradients. This filter is essential for effectively modeling the latent dynamics of the multi-omics data.

[0087] In a third step, an inverse compositional transform is implemented, such as the inverse isometric log ratio (ILR) transform or a softmax transform. The inverse ILR transform takes a binary tree and a matrix of (N x D-1) log-odd ratios as input and outputs a matrix of proportions. These proportions, with dimensions N x D, provide insights into the compositional nature of the biomarkers.

[0088] In a fourth step, an encoder neural network is designed that takes D-dimensional quantities (e.g., proportions, counts, intensities, mass spectra, molecules, proteins, transcripts, genes, genomes, concentrations, pixel values, and words) as input. The network projects these quantities onto a K-dimensional latent space, where K represents the dimensionality of the compressed space.

[0089] In a fifth step, a decoder neural network is constructed that utilizes an appropriate activation function for reconstructing the original input data. For microbiome sequencing count data, the inverse ILR transform coupled with Multinomial, Poisson, or Negative Binomial distribution are examples of appropriate activation functions. Other omics levels may require different activation functions (i.e. metabolomics decoders could benefit from an inverse ILR transform coupled with a Gaussian distribution). This network maps the K latent quantities back to the original D-dimensional space, effectively reconstructing the multi- omics measurements.

[0090] In a sixth step, an automatic differentiation framework is implemented that integrates modules 2, 4, and 5 into a single, fully differentiable model. This frameworkensures seamless gradient flow throughout the various components, enabling efficient training and optimization.

[0091] In a seventh step, the model is trained using a subset of the curated dataset from step 1 and validated on the remaining subset. This training process results in a trained machine learning model capable of predicting multi-omics measurements and clinical outcomes in future time points. The model incorporates information about confounders, clinical interventions, and previous multi-omics measurements.

[0092] By following these steps, various embodiments yield a powerful AI-driven model that can effectively analyze multi-omics data, capture latent dynamics, and predict clinical outcomes. The trained model can be applied to future data to enhance precision medicine, advance drug development, and improve patient care.

[0093] In various embodiments, the DVAE model is used in clinical applications. The DVAE model offers valuable capabilities for biomarker-guided patient stratification, enabling clinicians and researchers to make informed decisions about treatment approaches based on individual patient characteristics. With the trained DVAE model, users can predict clinical outcomes and future multi-omics measurements using available multi-omics data, clinical interventions, and confounders. This predictive capability empowers users to assess the likelihood of a patient's favorable response or negative outcomes, such as pathogenetic growth, inflammation, or neurological over-stimulation, before the actual clinical intervention takes place.

[0094] Additionally, the DVAE model provides a means to extract a subset of biomarkers that hold predictive power for patient response to specific clinical interventions. This valuable information enables the identification of key biomarkers associated with treatment efficacy or adverse reactions, facilitating personalized treatment selection. Furthermore, the DVAE model assists users in identifying subsets of biomarkers, including microbes,metabolites, proteins, and mRNA, that can be utilized for the design of new therapeutics. By leveraging the comprehensive insights gained from the DVAE model, researchers can target specific biomarkers for therapeutic development, potentially revolutionizing the field of drug discovery. Lastly, the DVAE model can be instrumental in designing future clinical trials. By leveraging the predictive capabilities and feature selection capabilities of the DVAE model, users can optimize the design of clinical trials, ensuring the inclusion of relevant biomarkers and patient cohorts that are most likely to yield meaningful insights and successful outcomes.

[0095] In various embodiments, the DVAE model can be used in additional applications. For example, the DVAE model can be used in designing industrial products for alleviating eutrophication in aquaculture farms. By leveraging large aquaculture multi-omics datasets that encompass a wide range of experimental interventions, the DVAE model can facilitate the identification of strategies that minimize eutrophication outcomes. This enables the development of innovative industrial products tailored to address the challenges associated with nutrient excess in aquaculture settings, promoting sustainable practices and improving environmental conditions.

[0096] In various embodiments, the DVAE model can be used in designing industrial products to reduce sludge in sewage treatment. Mining extensive multi-omics datasets from treatment plants, the DVAE model offers insights into the effects of various experimental interventions on sludge output. This information can guide the design of industrial products and processes aimed at reducing sludge generation, leading to more efficient and environmentally friendly sewage treatment systems.

[0097] In various embodiments, the DVAE model can be used in designing feed to reduce pathogenic infections in livestock without antibiotics. Leveraging large multi-omics datasets from livestock, including diverse experimental interventions, the DVAE modelfacilitates the identification of strategies to minimize mortality in livestock caused by pathogenic infections. This enables the development of specialized feed formulations that enhance the animals' resistance to infections, reducing the reliance on antibiotics and promoting healthier livestock farming practices.

[0098] Figure 6 is an exemplary plot 600 showing a proof-of-concept forecasting patient outcomes using a log-ratio constructed from two sets of microbes identified from the Shapley values generated from the model, in accordance with various embodiments.

[0099] Figure 6A is an exemplary diagram 610, showing a timeline of a typical FMT study, collecting biological samples x and patient outcomes w before and after the intervention u, in accordance with various embodiments.

[0100] Figure 7 is an exemplary diagram 700 showing the training procedure for the DVAE model, in accordance with various embodiments.

[0101] Figure 8 is an exemplary diagram 800 showing the usage procedure for the DVAE model, in accordance with various embodiments. System for creating and training a computer model

[0102] In various embodiments, a system for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally includes one or more processors. These one or more processors can be part of a single computer system, such as the computer system of Figure 1, or these one or more processors can be distributed across two or more computer systems.

[0103] The one or more processors perform a number of steps. In step (A), the one or more processors create a training dataset for at least one patient that includes a plurality of multi-omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data. In step (B), the one or moreprocessors create a differentiable Kalman filter module for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data. In step (C), the one or more processors create a second inverse compositional transform module for creating filtered multi-omics data from latent representations of the multi-omics data. In step (D), the one or more processors create a third encoder neural network module that encodes the matrix data, producing compressed data. In step (E), the one or more processors create a fourth decoder neural network module that for reconstructing the compressed data, producing original input data. In step (F), the one or more processors create a fifth automatic differentiation module that integrates the first, third, and fourth modules into a DVAE model. In step (G), the one or more processors train the model using a subset of the training dataset, apply hyper-parameter tuning to the model using another subset of the training dataset, and evaluate the model accuracy on a holdout dataset.

[0104] In various embodiments, the second inverse compositional transform module includes an inverse isometric log ratio (ILR) transform.

[0105] In various embodiments, the second inverse compositional transform module includes a softmax transform.

[0106] In various embodiments, the one or more processors further apply input data for a new patient to the trained model that includes a plurality of multi-omics data for the new patient and patient metadata that contains a plurality of confounder data, a plurality of intervention data and receive a plurality of predicted outcome data for the new patient from the model.

[0107] In various embodiments, the input data further includes a plurality of attributions for each biomarker and each predicted outcome for the new patient from the trained model. The plurality of attributions determines which biomarker contributed to the predicted patient responses. The attribution methods include Shapley values, integrated gradients, andGradCAM. Per-biomarker attributions are then used to construct additional models using techniques from compositional data analysis such as discriminative balance analysis.

[0108] In various embodiments, the model is described mathematically as ^^^ ^^௧^, ^^௧| ^^௧^^ ൌ ^^^^ ^^^^ ^^௧^^^, ^^^ ^^௧^| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^^௧, ^^^^^^ ^^௧| ^^௧ି^, ^^௧^^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^௧ି^^ ^^௧^^௧^^ ^^^, ^^^ ^^^ ^^௧^| ^^௧^, ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^^ ^^௧^, ^^௧^, ^^^^ where ^^௧ ^represents omics measurements for a given multi-omics modality j (aka microbial abundances across |X| microbial species), ^^௧^represents the latent representation of a measurement for omics modality j collected at time t, ^^௧represents the latent staterepresentation at time t, ^^௧^ represents clinical intervention r at time point t, ^^௧^ represents aclinical outcome measurement for patient outcome o at time t, ^^௧ representsconfounders at time point t and ^^^^௧^ represents a random intercept for a study k. ^^௧represents the transition matrix between latent states at time point t, ^^௧perturbation matrix at time point t, and ^^௧represents the projection matrix to obtain the measurements ^^௧from the latent state ^^௧. The functions ^^^and ^^^represent the encoder and decoder neural networks for omics modality j. Thethe outcome neural network for patient outcome o. Q, R are both pre-specified covariance matrices and ^^^is an estimable diagonal covariance matrix for omics modality j. ^^^represents a distribution such as the Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution, or Normal distribution for omics modality j. ^^^represents a distribution such as Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution, Bernoulli distribution, Binomial distribution, or Normal distribution for patient outcome o. This method can be fitted by minimizing the ELBO given by^^ ^^ ^^ ^^ ൌ ^^^^^ ^^, ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^^^^,௭|௫,^,௨^ ^^^^ ^^| ^^, ^^^ ^^^ ^^| ^^, ^^^ ^.

[0109] Inreduction as follows ^^^ ^^௧^, ^^௧| ^^௧^^ ൌ ^^^^ ^^^ ^^௧^^^, ^^^ ^^௧^| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^^௧, ^^^^^௧ି^^ ^^௧^^௧^^ ^^^, ^^^ ^^^ ^^௧^| ^^௧^, ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^ ^^௧^, ^^௧^, ^^^^ ^^^ ^^௧^| ^^௧^^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^^ ^^௧^^, ^^^^

[0110] where ^^௧ ^represents omics measurements for a given multi-omics modality j (aka microbial abundances across |X| microbial species), ^^௧^represents the latent representation ofa measurement for omics modality j collected at time t, ^^௧^ represents the measurements ofa intervention modality r collected at time t, ^^௧^represents the latent representation ofa intervention modality r collected at time t, ^^௧ represents the latent state representation attime t, ^^௧ represents clinical interventions across | ^^| possible interventions, ^^௧ representsconfounders at time point t and ^^^^௧^ represents a random intercept for a study k. ^^௧represents the transition matrix between latent states at time point t, ^^௧represents the perturbation matrix at time point t, and ^^௧represents the projection matrix to obtain the measurements ^^௧from the latent state ^^௧. The functions ^^^and ^^^represent the encoder and decoder neural networks for omics modality j. The^^^and ^^^represent the encoder and decoder neural networks for intervention modality r. Q, R are both pre-specified covariance matrices, ^^^is an estimable diagonal covariance matrix for omics modality j and ^^^is an estimable diagonal covariance matrix for intervention modality r. ^^^represents a measurement distribution such as the Multinomial distribution, Poisson distribution, Negativebinomial, Lognormal distribution or Normal distribution for omics modality j. ^^^represents a measurement distribution such as the Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution or Normal distribution for intervention modality r. ^^^represents a distribution such as Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution, Bernoulli distribution, Binomial distribution or Normal distribution for patient outcome o. This method can be fitted by minimizing the ELBO given by ^ ^.network to infer transition matrix ^^௧, perturbation matrix ^^௧and projection matrix ^^௧at time point t. Suitable neural networks include recurrence neural networks (RNNs), NeuralODEs, NeuralSDEs and Gaussian Processes.

[0112] In various embodiments, the one or more processors can handle omics modalities missing at given time points t, by performing imputation. This is performed by using the neural network in claim 7 to forecast both state ^^௧and latent representation ^^௧^at time point t and omics modality j. This method removes the constraint for all omics modalities to be measured at all available time points.

[0113] In various embodiments, multiple posterior draws can be sampled to perform statistical testing on the state ^^௧, latent representation ^^௧^, measurements ^^௧^and patient outcomes ^^௧^. Posterior draws can be used to quantify confidence intervals on estimated quantities ^^௧, ^^௧^, ^^௧^, ^^௧^. Furthermore, posterior draws can be used to estimate posterior predictive values to determine how likely the observed quantities ^^௧, ^^௧^, ^^௧^, ^^௧^were to be generated under the estimated DVAE model. Finally, these posterior draws can determine how quantities ^^௧, ^^௧^, ^^௧^, ^^௧^from different patients compare (i.e. determining if patientsfrom the responder group vs non-responder group have differing ^^௧, ^^௧^, ^^௧^, ^^௧^quantities).

[0114] In various embodiments, potential future scenarios can be forecasted from the DVAE model to inform future decisions. For instance, generating a simulation that altering the value of ^^௧^for a given intervention r at the current time t can generate future quantities ^^், ^^்^, ^^்^, ^^்^for time points T that are observed after the current time point t.

[0115] In various embodiments, counterfactual scenarios can be simulated from theDVAE model to perform causal inference tests. For instance, generating a simulationthat altering the value of ^^௧^ for a given intervention r at a previous time t can generatenew quantities ^^் , ^^்^ , ^^்^ , ^^்^ for time points T that are observed after time point t.

[0116] In various embodiments, the DVAE model can be used for companion diagnostics to predict patient outcomes post-intervention, using multi-omics data (i.e. fecal / vaginal / oral / skin microbial metagenomics, blood / urine / tumor / fecal metabolomics, blood / tumor proteomics, blood / tumor transcriptomics) from the patient pre-intervention. Interventions may include, but not limited to fecal matter transplants, or therapies derived from fecal matter transplants such as small molecule compositions, phage therapies, antibodies or live biotherapeutic products (LBPs). Patient outcomes may include, but not limited to tumor size, gastrointestinal symptoms questionnaires (i.e. GSRS), cytokine concentrations or behavioral questionnaires (i.e. CARS, ADOS, Vineland). This method can be applied to, but not limited to the following diseases : Crohn’s disease, Ulcerative Colitis, multi-drug resistant infections, irritable bowel syndrome, Graft vs Host disease, oncology (i.e. melanoma, lung cancer, brain cancer, pancreatic cancer, …), diabetes, Cirrhosis, constipation, depression, Parkinsons’ disease, autism, HIV, diarrhea, Hepatic Encephalopathy, Alcoholic hepatitis, multiple sclerosis, arthritis, liver failure, malnutrition, pancreatitis, urinary tract infection, anorexia,alopecia, chronic fatigue syndrome, Chronic obstructive pulmonary disease (COPD), NASH, atopic dermatitis, food allergy, and Tourette's syndrome.

[0117] In various embodiments, the DVAE model can be used to construct companion diagnostics to identify patients that are likely to respond to a given drug. These companion diagnostics can be used to specify patient inclusion criteria or exclusion criteria in clinical trials. An example of this is constructing a diagnostic that detects short chain fatty acids in patient stool; this short chain fatty acid diagnostic can be then used to identify patients that are likely to respond to immunotherapy.

[0118] In various embodiments, the DVAE model can be used to construct companion diagnostics that equip clinicians with the necessary insights to prescribe appropriate medications based on individual patient biomarkers. An example of this is constructing a diagnostic that detects short chain fatty acids in patient stool; this short chain fatty acid diagnostic can be then used to determine if a patient should be recommended to undergo immunotherapy based on their short chain fatty acid levels.

[0119] In various embodiments, the DVAE model enables the identification of drug candidates from fecal matter transplants by attributing specific biomarkers in the donor stool to the patient's response. These biomarker attributions can be computed using techniques such as Shapley values, integrated gradients or GradCAM. These biomarker attributions can then be used to prioritize which biomarkers to extract from the donor stool to include in a drug product. Examples of biomarkers that can be extracted from donor stool include cultured microbes, isolated small molecules or phages.Method for creating and training a computer model

[0120] Figure 9 is a flowchart showing a method 900 for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, in accordance with various embodiments.

[0121] In step 910 of method 900, a training dataset is created for at least one patient that includes a plurality of multi-omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data.

[0122] In step 920, a differentiable Kalman filter module is created for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data.

[0123] In step 930, a second inverse compositional transform module is created for creating filtered multi-omics data from latent representations of the multi-omics data.

[0124] In step 940, a third encoder neural network module is created that encodes the matrix data, producing compressed data.

[0125] In step 950, a fourth decoder neural network module is created for reconstructing the compressed data, producing original input data.

[0126] In step 960, a fifth automatic differentiation module is created that integrates the first, third, and fourth modules into a dynamic variational autoencoder (DVAE) model.

[0127] In step 970, the model is trained using a subset of the training dataset, hyper- parameter tuning is applied to the model using another subset of the training dataset, and the model accuracy is evaluated on a holdout dataset. Computer program product for creating and training a computer model

[0128] In various embodiments, computer program products include a tangible computer- readable storage medium whose contents include a program with instructions being executedon a processor so as to perform a method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally. This method is performed by a system that includes one or more distinct software modules.

[0129] Figure 10 is a schematic diagram of a system 1000 that includes one or more distinct software modules that perform a method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, in accordance with various embodiments. System 1000 includes input module 1010 and analysis module 1020.

[0130] Input module 1010, in step (A), creates a training dataset for at least one patient that includes a plurality of multi-omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data.

[0131] Analysis module 1020, in step (B), creates a differentiable Kalman filter module for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data.

[0132] Analysis module 1020, in step (C), creates a second inverse compositional transform module for creating filtered multi-omics data from latent representations of the multi-omics data.

[0133] Analysis module 1020, in step (D), creates a third encoder neural network module that encodes the matrix data, producing compressed data.

[0134] Analysis module 1020, in step (E), creates a fourth decoder neural network module for reconstructing the compressed data, producing original input data.

[0135] Analysis module 1020, in step (F), creates a fifth automatic differentiation module that integrates the first, third, and fourth modules into a dynamic variational autoencoder (DVAE) model.

[0136] Analysis module 1020, in step (G), trains the model using a subset of the training dataset, applies hyper-parameter tuning to the model using another subset of the training dataset, and evaluates the model accuracy on a holdout dataset.

[0137] While the present teachings are described in conjunction with various embodiments, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art.

[0138] Further, in describing various embodiments, the specification may have presented a method and / or process as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and / or process should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the various embodiments.

Claims

WHAT IS CLAIMED IS:

1. A method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, comprising: creating a training dataset for at least one patient that includes a plurality of multi-omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data; creating a differentiable Kalman filter module for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data; creating a second inverse compositional transform module for creating filtered multi- omics data from latent representations of the multi-omics data; creating a third encoder neural network module that encodes the matrix data, producing compressed data; creating a fourth decoder neural network module for reconstructing the compressed data, producing original input data; creating a fifth automatic differentiation module that integrates the first, third, and fourth modules into a dynamic variational autoencoder (DVAE) model; and training the model using a subset of the training dataset, applying hyper-parameter tuning to the model using another subset of the training dataset, and evaluating the model accuracy on a holdout dataset.

2. The method of claim 1, wherein the second inverse compositional transform module comprises an inverse isometric log ratio (ILR) transform.

3. The method of claim 1, wherein the second inverse compositional transform module comprises a softmax transform.

4. The method of claim 1, further comprising applying input data for a new patient to the trained model that includes a plurality of multi-omics data for the new patient and patient metadata that contains a plurality of confounder data, a plurality of intervention data and receiving a plurality of predicted outcome data for the new patient from the model.

5. The method of claim 4, wherein the input data further includes a plurality of attributions for each biomarker and each predicted outcome for the new patient from the trained model, wherein the plurality of attributions determines which biomarker contributed to the predicted patient responses, and wherein attribution methods include Shapley values, integrated gradients, and GradCAM, and wherein per-biomarker attributions are then used to construct additional models using techniques from compositional data analysis such as discriminative balance analysis.

6. The method of claim 1, wherein the model is described mathematically as ^^^ ^^௧^, ^^௧| ^^௧^^ ൌ ^^^^ ^^^^ ^^௧^^^, ^^^ ^^௧^| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^^௧, ^^^^^^ ^^௧^| ^^௧^, ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^^ ^^௧^, ^^௧^, ^^^^ where ^^௧ ^represents omics measurements for a given multi-omics modality j (aka microbial abundances across |X| microbial species), ^^௧^represents the latent representation of a measurement for omics modality j collected at time t, ^^௧represents the latent state representation at time t, ^^௧^represents clinical intervention r at time point t, ^^௧^ represents a clinical outcome measurement for patient outcome o attime t, ^^௧ represents confounders at time point t, ^^^^௧^ represents a randomintercept for a study k, ^^௧represents the transition matrix between latent states at timepoint t, ^^௧represents the perturbation matrix at time point t, ^^௧represents the projection matrix to obtain the measurements ^^௧from the latent state ^^௧, the functions ^^^and ^^^represent the encoder and decoder neural networks for omics modality j, the function ^^^represents the outcome neural network for patient outcome o, Q, R are both pre-specified covariance matrices, ^^^is an estimable diagonal covariance matrix for omics modality j, ^^^represents a distribution such as the Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution or Normal distribution for omics modality j, and ^^^represents a distribution such as Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution, Bernoulli distribution, Binomial distribution or Normal distribution for patient outcome o, wherein the method is fitted by minimizing the ELBO given by ^^ ^^ ^^ ^^ ൌ ^^^^^ ^^, ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^^^^,௭|௫,^,௨^^^^^ ^^^ ^^^ ^^^ ^- 7. The method of claim 6, where the model is further described mathematically to perform dimensionality reduction on the interventional data as follows ^^^ ^^௧^, ^^௧| ^^௧^^ ൌ ^^^^ ^^^ ^^௧^^^, ^^^ ^^௧^| ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^௧^^^௧, ^^^ ^^^ ^^௧^| ^^௧.^ ൌ ^^^^ ^^^^ ^^௧.^^, ^^^ ^^௧^| ^^௧^^ ൌ ^^^^ ^^^^ ^^௧^^^,ൌ ^^௧^^௧ି^^ ^^௧^^௧^^ ^^^, ^^^ ^^^ ^^௧^| ^^௧^, ^^௧^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^ ^^௧^, ^^௧^, ^^^^ ^^^ ^^௧^| ^^௧^^ ൌ ^^ ^^ ^^ ^^ ^^ ^^^ ^^^^ ^^௧^^, ^^^^ where ^^௧ ^represents omics measurements for a given multi-omics modality j (aka microbial abundances across |X| microbial species), ^^௧^represents the latentrepresentation of a measurement for omics modality j collected at time t, ^^௧^represents the measurements of a intervention modality r collected at time t,^^௧^ represents the latent representation of a intervention modality r collected attime t, ^^௧ represents the latent state representation at time t, ^^௧ represents clinicalinterventions across | ^^| possible interventions, ^^௧ represents confounders at timepoint t, ^^^^௧^ represents a random intercept for a study k, ^^௧ represents the transitionmatrixlatent states at time point t, ^^௧represents the perturbation matrix at time point t, and ^^௧represents the projection matrix to obtain the measurements ^^௧from the latent state ^^௧, the functions ^^^and ^^^represent the encoder and decoder neural networks for omics modality j, the functions ^^^and ^^^represent the encoder and decoder neural networks for intervention modality r, Q, R are both pre-specified covariance matrices, ^^^is an estimable diagonal covariance matrix for omics modality j and ^^^is an estimable diagonal covariance matrix for intervention modality r, ^^^represents a measurement distribution such as the Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution or Normal distribution for omics modality j, ^^^represents a measurement distribution such as the Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution or Normal distribution for intervention modality r, and ^^^represents a distribution such as Multinomial distribution, Poisson distribution, Negative binomial, Lognormal distribution, Bernoulli distribution, Binomial distribution or Normal distribution for patient outcome o, wherein the method is be fitted by minimizing the ELBO given by ^^ ^^ ^^ ^^ ൌ ^^^^^ ^^, ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^ ^^^ ^^| ^^^^- 8. The method of claim 6, further comprising using a neural network to infer transition matrix ^^௧, perturbation matrix ^^௧and projection matrix ^^௧at time point t, wherein the neural network includes recurrence neural networks (RNNs), NeuralODEs, NeuralSDEs, and Gaussian Processes. - 9. The method of claim 6, further comprising performing imputation to handle omics modalities missing at given time points t by using a neural network to forecast both state ^^௧and latent representation ^^௧^at time point t and omics modality j, wherein the method removes the constraint for all omics modalities to be measured at all available time points. - 10. The method of claim 6, wherein multiple posterior draws are sampled to perform statistical testing on the state ^^௧, latent representation ^^௧^, measurements ^^௧^and patient outcomes ^^௧^, wherein posterior draws are used to quantify confidence intervals on estimated quantities ^^௧, ^^௧^, ^^௧^, ^^௧^, wherein the posterior draws are used to estimate posterior predictive values to determine how likely the observed quantities ^^௧, ^^௧^, ^^௧^, ^^௧^were to be generated under the model, and wherein the posterior draws determine how quantities ^^௧, ^^௧^, ^^௧^, ^^௧^from different patients compare. - 11. The method of claim 6, wherein scenarios are forecasted from the model to inform future decisions, wherein a simulation is generated that alters the value of ^^௧^for a given intervention r at a the current time t can generate future quantities ^^், ^^்^, ^^்^, ^^்^for time points T that are observed after the current time point t.- 12. The method of claim 6, wherein counterfactual scenarios are be simulated from the model to perform causal inference tests by generating a simulation that altering the value of ^^௧^for a given intervention r at a previous time t can generate new quantities ^^், ^^்^, ^^்^, ^^்^for time points T that are observed after time point t. - 13. The method of claim 1, wherein the model is used predict patient outcomes post-intervention, using multi-omics data from the patient pre-intervention, wherein an intervention is a fecal matter transplant, or a therapy derived from a fecal matter transplant such as small molecule compositions, phage therapies, antibodies, or live biotherapeutic products (LBPs), wherein patient outcomes comprise tumor size, gastrointestinal symptoms questionnaires (i.e. GSRS), cytokine concentrations or behavioral questionnaires (i.e. CARS, ADOS, Vineland), wherein the is applied to, Crohn’s disease, Ulcerative Colitis, multi-drug resistant infections, irritable bowel syndrome, Graft vs Host disease, oncology, diabetes, Cirrhosis, constipation, depression, Parkinsons’ disease, autism, HIV, diarrhea, Hepatic Encephalopathy, Alcoholic hepatitis, multiple sclerosis, arthritis, liver failure, malnutrition, pancreatitis, urinary tract infection, anorexia, alopecia, chronic fatigue syndrome, Chronic obstructive pulmonary disease (COPD), NASH, atopic dermatitis, food allergy, or Tourette's syndrome. - 14. A system method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, comprising:one or more processors that (a) create a training dataset for at least one patient that includes a plurality of multi-omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data, (b) create a differentiable Kalman filter module for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data, (c) create a second inverse compositional transform module for creating filtered multi-omics data from latent representations of the multi-omics data, (d) create a third encoder neural network module that encodes the matrix data, producing compressed data, (e) create a fourth decoder neural network module for reconstructing the compressed data, producing original input data, (f) create a fifth automatic differentiation module that integrates the first, third, and fourth modules into a dynamic variational autoencoder (DVAE) model, and (g) train the model using a subset of the training dataset, apply hyper-parameter tuning to the model using another subset of the training dataset, and evaluate the model accuracy on a holdout dataset.

15. A computer program product, comprising a non-transitory tangible computer- readable storage medium whose contents cause a processor to perform a method for creating and training a computer model for determining a clinical outcome from multi-omics data collected longitudinally, comprising:providing a system, wherein the system comprises one or more distinct software modules, and wherein the distinct software modules comprise an input module and an analysis module; (a) creating a training dataset for at least one patient that includes a plurality of multi- omics data, and patient metadata that contains a plurality of confounder data, a plurality of intervention data and a plurality of patient outcome data using the input model; (b) creating a differentiable Kalman filter module for modeling the latent dynamics of input multi-omics data, producing latent representations of multi-omics data using the analysis module; (c) creating a second inverse compositional transform module for creating filtered multi- omics data from latent representations of the multi-omics data using the analysis module; (d) creating a third encoder neural network module that encodes the matrix data, producing compressed data using the analysis module; (e) creating a fourth decoder neural network module for reconstructing the compressed data, producing original input data using the analysis module; (f) creating a fifth automatic differentiation module that integrates the first, third, and fourth modules into a dynamic variational autoencoder (DVAE) model using the analysis module; and (g) training the model using a subset of the training dataset, applying hyper-parameter tuning to the model using another subset of the training dataset, and evaluating the model accuracy on a holdout dataset using the analysis module.

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