Residual semi-recurrent neural network

Abstract

A residual semi-recurrent neural network (RSNN) can be configured to receive time-invariant input and time-varying input data to generate one or more time series predictions. The time-invariant input can be processed by a multilayer perceptron of the RSNN. The output of the multilayer perceptron can be used as an initial state of a recurrent neural network unit of the RSNN. The recurrent neural network unit can also receive the time-invariant input and process the time-invariant input using the time-invariant input to generate an output. The outputs of the multilayer perceptron and the recurrent neural network unit can be combined to generate the one or more time series predictions.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application No. 62 / 824,895, filed on March 27, 2019, and European Patent Application No. 19305611.6, filed on May 13, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates to artificial neural networks. Background Art

[0004] Artificial neural networks (ANNs) are computing systems inspired in part by biological neural networks. An ANN is a framework in which one or more machine learning algorithms work together to process complex data inputs. ANNs can learn to perform tasks, such as image recognition, where the ANN learns to distinguish certain features in an image (e.g., animals, vehicles, road signs, etc.). An ANN typically consists of a number of connected nodes called artificial neurons. Each connection transmits a signal from one artificial neuron to another. The artificial neuron that receives the signal can process it and then output the result to the other artificial neurons connected to it.

[0005] In a typical embodiment, the signals at the connections between artificial neurons (the connections are sometimes called edges) are real numbers, and the output of each artificial neuron is calculated as a nonlinear function of the sum of its inputs. Artificial neurons and edges typically have weights that can be adjusted when training the ANN. ANNs have been used for various tasks such as computer vision, speech recognition, machine translation, and medical diagnosis. Recently, ANNs have been used as predictive models for predicting outcomes based on certain inputs. For example, ANNs can be used for drug kinetic modeling to predict how a drug will interact with the human body (e.g., the time course of drug absorption, distribution, metabolism, and excretion). Summary of the Invention

[0006] At least one aspect of the present disclosure provides a neural network. The neural network includes a multilayer perceptron (MLP) configured to receive a first type of external data and process the first type of external data to generate an MLP output. The neural network includes a recurrent neural network (RNN) unit. The RNN unit is configured to receive at least a portion of the MLP output and a second type of external data. The RNN unit is configured to process at least a portion of the MLP output and at least the second type of external data to generate an RNN output. The MLP and RNN units are collectively configured to generate one or more time series forecasts based at least in part on the RNN output and the MLP output.

[0007] The MLP may include an input layer, at least one hidden layer, and an output layer. The RNN unit may include at least one RNN hidden layer. The RNN unit may include a long short-term memory RNN unit. The RNN unit may include a conventional RNN unit. The RNN unit may include a gated recurrent unit.

[0008] The first type of external data may include time-invariant data. The second type of external data may include time-varying data.

[0009] The neural network can be configured to combine the MLP output with the RNN output to generate a residual output. One or more time series predictions can be generated based at least in part on the residual output. The one or more time series predictions can include concentration values ​​of the drug in plasma as a function of time after administration of a dose of the drug.

[0010] At least one other aspect of the present disclosure provides a method. The method includes receiving, by an MLP, a first type of external data. The method includes processing, by the MLP, the first type of external data to generate an MLP output. The method includes receiving, by an RNN unit, at least a portion of the MLP output and a second type of external data. The method includes processing, by the RNN unit, at least a portion of the MLP output and the second type of external data to generate an RNN output. The method includes generating one or more time series forecasts based, at least in part, on the RNN output and the MLP output.

[0011] The first type of external data may include time-invariant data. The second type of external data may include time-varying data.

[0012] The method may further include combining the MLP output with the RNN output to generate a residual output. One or more time series predictions may be generated based at least in part on the residual output. The one or more time series predictions may include concentration values ​​of the drug in plasma as a function of time after administration of a dose of the drug.

[0013] The RNN unit may include a long short-term memory RNN unit. The RNN unit may include a conventional RNN unit. The RNN unit may include a gated recurrent unit.

[0014] Embodiments of the present disclosure may include one or more of the following advantages. Compared to traditional neural networks (e.g., recurrent neural networks and convolutional neural networks), the described neural networks can process time-varying data and time-invariant data in a computationally efficient manner to generate accurate time series forecasts. Compared to traditional neural networks, the output of a particular neural network layer can be combined with the output of consecutive neural network layers to improve forecast accuracy. Compared to traditional neural networks, the described neural networks can better capture the relationship between time-varying data and time-invariant data, and how this relationship affects the final time series forecast.

[0015] These and other aspects, features, and embodiments may be expressed as methods, apparatus, systems, components, program products, means, or steps for performing the functions, among other ways.

[0016] These and other aspects, features and embodiments will be apparent from the following description, including the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG1 shows a diagram depicting a residual semi-recurrent neural network according to one or more embodiments of the present disclosure.

[0018] FIG2A shows a diagram depicting a recurrent neural network unit according to one or more embodiments of the present disclosure.

[0019] Figure 2B shows a diagram depicting an unfolded recurrent neural network unit according to one or more embodiments of the present disclosure.

[0020] FIG3 is a diagram depicting the architecture of a residual semi-recurrent neural network according to one or more embodiments of the present disclosure.

[0021] 4 is a flow chart depicting a method for generating one or more time series forecasts using time-varying data and time-invariant data according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0022] The use of artificial neural networks (ANNs) as predictive models to predict future outcomes based on some external data is becoming increasingly popular. For example, pharmacokinetic (PK) modeling is a key step in drug development, simulating how a drug interacts with the human body (e.g., the time course of drug absorption, distribution, metabolism, and excretion). In some pharmacokinetic modeling approaches, time-invariant data (e.g., baseline patient characteristics (e.g., age, sex, etc.)) and time-varying data (e.g., the dose level of the drug administered to the patient) are used to generate a PK curve, which shows the concentration of the drug in plasma over a time interval. Traditionally, differential equations, borrowed from the field of fluid dynamics, have been used to model the interactions between drugs and the human body. Differential equations may help describe the underlying physical processes that occur in the human body after receiving a drug dose; however, they may not account for all the heterogeneity between patients. Therefore, predictions for individual patients obtained using these differential equations may be imprecise, whereas predictions at the population level may be accurate.

[0023] A common approach to improving the predictive accuracy of pharmacokinetic modeling often involves the use of feedforward neural networks (e.g., convolutional neural networks). However, despite improved predictive accuracy compared to traditional differential equation approaches, feedforward neural networks may not be able to account for correlations between pharmacokinetic measurements taken for the same individual at multiple time points. This is because traditional feedforward networks typically process information in only one direction (e.g., from the input layer, through the hidden layers, to the output layer), and therefore only consider the current input without any concept of temporal order.

[0024] Recurrent neural networks (RNNs) have been shown to be better at processing time-varying data because these neural networks include nodes with connections that form a directed graph along the time series, allowing the RNN to process the input sequence using internal memory. However, when using traditional RNNs to process time-invariant data, the RNN may process the time-invariant data in a manner similar to that of time-varying data. This may generate a large amount of unnecessary duplicate data and lead to poor prediction performance, especially when using small sample sizes. Therefore, an artificial neural network is desired that is adapted to efficiently process time-invariant and time-varying data to generate time-based predictions with higher accuracy than traditional methods.

[0025] The present disclosure provides a residual semi-cyclic neural network that is configured to process time-invariant data and time-varying data in an efficient manner, which improves prediction accuracy compared to traditional RNNs and feedforward networks. The residual semi-cyclic neural network includes a multilayer perceptron (MLP) for receiving and processing time-invariant data. The residual semi-cyclic neural network also includes an RNN unit for processing time-varying data. The outputs from the MLP and RNN units are used by the neural network to generate one or more time series predictions. For example, if used for PK modeling, data related to the patient's baseline characteristics are provided to the MLP, and data related to the drug dosage level administered to the patient at a sequential time point is provided to the RNN. The output of the MLP can be used as the initial state of the RNN. The outputs of the RNN and the MLP can also be combined to generate a PK curve that shows the relationship between the drug concentration in the patient's plasma and the time after a single dose of the drug is administered to the patient.

[0026] In the following description, for the purpose of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent that the present disclosure may be implemented without these specific details. In other examples, well-known structures and devices are shown in block diagram form to avoid unnecessarily obscuring the present disclosure.

[0027] In the accompanying drawings, for ease of description, a specific arrangement or ordering of schematic elements is shown, such as the arrangement or ordering of representative devices, modules, instruction blocks, and data elements. However, it should be understood by those skilled in the art that the specific order or arrangement of schematic elements in the accompanying drawings does not mean that a specific processing order or process separation is required. Furthermore, the inclusion of schematic elements in the accompanying drawings does not mean that such elements are required in all embodiments, or that the features represented by such elements may not be included in other elements or may not be combined with other elements in some embodiments.

[0028] Further, in the accompanying drawings, connecting elements, such as solid or dotted lines or arrows, are used to illustrate the connection, relationship or association between two or more other schematic elements, and the lack of any such connecting element does not mean that there is no connection, relationship or association. In other words, some connections, relationships or associations between elements are not shown in the accompanying drawings, so as not to confuse the present disclosure. In addition, for ease of illustration, a single connecting element is used to represent multiple connections, relationships or associations between elements. For example, in the case where a connecting element represents the communication of a signal, data or instruction, it will be understood by those skilled in the art that this element represents one or more signal paths (e.g., buses), as may be needed, to affect communication.

[0029] Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, it will be apparent to one of ordinary skill in the art that the various described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail to avoid unnecessarily obscuring aspects of the embodiments.

[0030] Several features are described below, each of which can be used independently of one another or in any combination with the other features. However, any single feature may not address all of the issues discussed above, or may address only one of the issues discussed above. Some of the issues discussed above may not be fully addressed by any of the features described herein. Although headings are provided, data related to a particular heading but not found in the section with that heading may also be found elsewhere in this specification.

[0031] As used herein, the term processing, as used in conjunction with a given neural network layer / unit, refers to the known neural network process of applying learned weights / activation functions corresponding to each neuron included in the given neural network layer / unit to input data to produce an output for each neuron. As is known in the art, the learned weights / activation functions can be adjusted / tuned by using a training data set to teach the neural network to associate certain features of the data set with certain outcomes.

[0032] System Overview:

[0033] FIG1 shows a diagram depicting a residual semi-recurrent neural network 100 according to one or more embodiments of the present disclosure. The residual semi-recurrent neural network (RSNN 100) includes an MLP 110 and an RNN unit 120. The MLP 110 includes an input layer 111, a hidden layer 112, and an output layer 113. The RNN unit 120 includes an RNN hidden layer 122 and an RNN output layer 123. The MLP 110 is communicatively coupled to the RNN unit 120.

[0034] The input layer 111 of the MLP 110 includes a first input neuron 111a and a second input neuron 111b. The hidden layer 112 of the MLP 110 includes a first hidden neuron 112a, a second hidden neuron 112b, and a third hidden neuron 112c. The output layer 113 of the MLP 110 includes a first output neuron 113a and a second output neuron 113b. The layers 111, 112, 113 of the MLP 110 are fully connected, meaning that every neuron in a given layer is connected to every neuron in the successive layers. For example, the first output neuron 113a is connected to the first hidden neuron 112a, the second hidden neuron 112b, and the third hidden neuron 112c.

[0035] Although MLP 110 includes one hidden layer 112, in some embodiments, MLP 110 includes more hidden layers (e.g., two hidden layers, three hidden layers, etc.) Each of layers 111, 112, and 113 may include more or fewer neurons than shown in the illustrated embodiment.

[0036] The input layer 111 is configured to receive time-invariant data and send the time-invariant data to the hidden layer 112. Examples of time-invariant data may include values ​​associated with one or more patient baseline characteristics, such as the patient's age and / or gender. Each of the hidden nodes 112a, 112b, and 112c of the hidden layer 112 receives the time-invariant data and processes the time-invariant data to generate an output. The output of each of the hidden nodes 112a, 112b, and 112c of the hidden layer 112 is sent to each of the output nodes 113a and 113b. The output nodes 113a and 113b process the received output using their activation functions to generate the MLP output.

[0037] The MLP 110 sends the MLP output to the RNN unit 120. The RNN hidden layer 122 receives the MLP output. In this way, the MLP output is used as the initial state of the RNN unit 120. The RNN hidden layer 122 is also configured to receive time-varying input data. As will be explained in more detail later with reference to Figure 3, the RNN unit 120 is configured to sequentially process the received time-varying data while using the MLP output from the MLP 110 as an initial state to generate one or more time series predictions. For example, the MLP output can be generated by processing input data associated with the patient's baseline characteristics, and the time-invariant data can be a sequence of the cumulative amount of the drug injected into the patient. In this example, the output of the RNN unit (time series prediction) can be a PK curve. In some embodiments, the RSNN 100 is configured to add the output of the MLP 110 to the output of the RNN unit 120 to generate a time series prediction.

[0038] Although shown as having one hidden layer 122, in some embodiments, the RNN unit 120 has additional RNN hidden layers. In such instances, the MLP 110 can be configured to provide its output to one or more additional RNN hidden layers. In some embodiments, the RSNN 100 includes additional fully connected layers between the MLP unit 110 and the RNN unit 120. In these instances, the MLP 110 can be configured to provide its output to one or more additional fully connected layers. The number of additional RNN hidden layers and fully connected layers can be based on processing requirements, efficiency factors, and practical considerations, such as the type and amount of data being processed.

[0039] FIG2A shows a diagram depicting an RNN unit 200 according to one or more embodiments of the present disclosure. The RNN unit 200 includes an RNN input layer 210, an RNN hidden layer 211, and an RNN output layer 212. The RNN input layer 210 includes a first RNN input neuron 210a, a second RNN input neuron 210b, and a third RNN input neuron 210c. In some embodiments, the RNN input layer 210 is the output layer of the previous MLP.

[0040] The RNN hidden layer 211 is configured to receive the output from the RNN input layer 210. As previously described with reference to FIG1 , the output from the RNN input layer can serve as the initial state for the RNN hidden layer 211. The RNN hidden layer 211 includes a first recurrent neuron 211a and a second recurrent neuron 211b. Each of the RNN input neurons 210a, 210b, and 210c is connected to each of the recurrent neurons 211a and 211b. Each of the recurrent neurons 211a and 211b is configured to receive a first sequential data point, process the first sequential data point to generate a first output, and use the first output to process consecutive sequential data points. For example, suppose the sequential data points are the cumulative amount of a drug injected into a patient. The first sequential data point can be the cumulative amount at a first time, and the second sequential data point can be the cumulative amount at a second time that occurs after the first time. The recurrent neurons 211a and 211b will receive the first sequential data point, process the first sequential data point to generate a first output, and use information from the first output to process the second sequential data point.

[0041] The RNN output layer 212 is configured to receive the output from the hidden layer 211. The RNN output layer 212 includes a first RNN output neuron 212a, a second RNN output neuron 212b, a third RNN output neuron 212c, and a fourth RNN output neuron 212d. Each of the RNN output neurons 212a, 212b, 212c, and 212d is connected to each of the recurrent neurons 211a and 211b.

[0042] 2B shows a diagram depicting an expanded recurrent neural network unit 300 according to one or more embodiments of the present disclosure. As shown, the RNN hidden layer 321 is configured to receive and process a first sequence input 310a to generate a first output (S1). The RNN hidden layer 321 is also configured to receive a second sequence input 310b following the first sequence input 310a. The RNN hidden layer 321 uses the output (S1) associated with the first sequence input 310a to process the second sequence input 310b to generate a second output (S2). Similarly, the RNN hidden layer 321 is configured to use the second output (S2) to process a third sequence input 310c following the second sequence input 310b to generate a third output (S3).

[0043] 3 is a diagram depicting the architecture of an RSNN 400 according to one or more embodiments of the present disclosure. RSNN 400 includes an MLP layer 410 and an RNN hidden layer 422. MLP 410 is configured to receive a time-invariant input 410. For example, the time-invariant input 410 may correspond to a patient's baseline characteristics, such as age, gender, etc. MLP 410 processes the invariant input 410 to generate an MLP output (S0), which is used as the initial state of the RNN hidden layer 422. RNN hidden layer 422 receives a first sequence input 420a and uses the MLP output (S0) to process the first sequence input 420a to generate a first RNN output (S1). RNN hidden layer 422 then receives a second sequence input 420b and uses the first RNN output (S1) to process the second sequence input 420b and generate a second RNN output (S2). The RNN hidden layer 422 then receives the third sequence input 420c and processes the third sequence input 420c using the second RNN output (S2) to generate a third RNN output (S3). The MLP output (S0) is then added 430 to the third RNN output (S3) to generate a time series prediction 440. In some embodiments, the sequence input corresponds to the cumulative amount of drug injected at a given time. In some embodiments, the time series prediction 440 is a PK curve.

[0044] Although the RNN units shown and described above are conventional RNN units, other types of RNN units may also be used. In some embodiments, a long short-term memory (LSTM) RNN unit is used. An LSTM RNN unit refers to an RNN unit that includes a unit, an input gate, an output gate, and a forget gate. The unit memorizes values ​​within an arbitrary time interval, and the three gates control the flow of information. It is known that the gradient vanishing problem is encountered in certain instances when training traditional RNNs, and the LSTM RNN unit can minimize the impact of the gradient vanishing problem. In some embodiments, a gated recurrent unit (GRU) is used as an RNN unit. GRU is an LSTM with a forget gate, but it has fewer parameters than LSTM because it does not have an output gate. Compared to LSTM, GRU exhibits better prediction performance when processing relatively small data sets.

[0045] 4 is a flow chart depicting a method 500 for generating one or more time series forecasts using time-varying data and time-invariant data according to one or more embodiments of the present disclosure. The method 500 includes receiving a first type of external data by an MLP (block 502); processing the first type of external data by the MLP to generate an MLP output (block 504); receiving at least a portion of the MLP output and a second type of external data by an RNN unit (block 506); processing at least a portion of the MLP output and the second type of external data by the RNN unit to generate an RNN output (block 508); and generating one or more time series forecasts based at least in part on the RNN output and the MLP output.

[0046] At block 502, the MLP of the RSNN receives a first type of external data. In some embodiments, the first type of external data is time-invariant data. For example, the time-invariant data may be patient baseline characteristics.

[0047] At block 504 , the MLP processes the first type of external data to generate an MLP output, as previously described with reference to FIG. 1 .

[0048] At block 506, the RNN unit of the MLP receives at least a portion of the MLP output from the MLP. The RNN unit also receives a second type of external data. In some embodiments, the second type of external data is time-varying data. For example, the time-varying data may be a sequence of cumulative amounts of a drug injected into a patient.

[0049] At block 508 , the RNN unit processes the received portion of the MLP output and the second type of external data to generate the RNN output, as previously described with reference to FIG. 3 .

[0050] At block 510, the RSNN generates one or more time series predictions based at least in part on the RNN output and the MLP output. In some embodiments, the RSNN combines the RNN output with the MLP output to generate one or more time series predictions. The time series predictions can be, for example, a PK curve.

[0051] Example method for training RSNN:

[0052] An example method for training an RSNN for pharmacokinetic modeling will now be described. Training and validating RSNN as a pharmacokinetic model in is the input of the model. i is a p-dimensional vector representing the p baseline characteristics of the i-th patient, and d i is the time series of the actual dose levels assigned to the i-th patient. irepresents the output from the model, i.e., the time series of observed pharmacokinetic concentrations of patient i. The model is iteratively trained using patients from the training set. During the training process, the model generates predictions c i With the true value data c i Compare them and update their weights accordingly.

[0053] When training the model For a given instance i, the input sequence consists of and, in Do not change over time because they are time-invariant baseline characteristics.

[0054] The baseline features are provided to the multi-layer perceptron (MLP) of the RSNN. The output of the MLP is then used as the initial state of the traditional RNN unit of the RSNN. Time-varying data (e.g., the dose level assigned to the patient and the given time) are provided to the traditional RNN unit. Because time-invariant inputs may have a greater impact on the PK model than time-varying inputs, a shortcut connection is implemented between the MLP for processing time-invariant inputs and the fully connected layer stacked on top of the recurrent layer. This shortcut connection provides a way to propagate the information contained in the time-invariant input directly to the final output of the RNN unit.

[0055] Mathematically, RSNN is defined as follows. For a given instance i, the instantaneous invariant input x i and the time-varying input sequence Output sequence Obtained through the following

[0056] s i0 =σ(Tx i +c), (1)

[0057] s it =σ(Uz it +Ws i，t-1 +b), t=1, ..., T i , (2)

[0058]

[0059] The first equation (1) defines the fully connected layer of the MLP. and are the parameters to be trained.

[0060] For pharmacokinetic modeling, the relationship z it =d itSimilarly, an MLP may contain more than one fully-connected layer. Furthermore, when there is more than one recurrent layer in an RNN cell, the initial states of only the first recurrent layer, only the last recurrent layer, or all recurrent layers may be the output of the MLP. Additionally, when there is more than one fully-connected layer stacked on top of a recurrent layer, the output of the MLP may be provided to only the first fully-connected layer, only the last fully-connected layer, or all fully-connected layers. These different design decisions can be considered hyperparameters.

[0061] Experimental results:

[0062] A dataset consisting of 65 patients was fed to an example RSNN using a gated recurrent neural network (GRU) as the RNN unit. For each patient, the observed PK value sequence (y i ), two baseline characteristics (x i ) i.e. age and gender, and the cumulative amount of injected drugs (d i ). Use GRU to connect the input and output of each time point of the RSNN of the dataset and fit the results of the training set and validation set (e.g., PK curve).

[0063] The RSNN model accurately fit all PK curves in the validation set, including two very peaked PK curves seen in the training set. This demonstrates that the RSNN is able to capture the complex nonlinear relationship between PK values ​​and the cumulative amount of injected drug, as well as baseline characteristics.

[0064] In the foregoing description, embodiments of the present disclosure have been described with reference to many specific details, which may vary from embodiment to embodiment. Accordingly, the specification and drawings are to be regarded as illustrative rather than restrictive. The sole and exclusive indicator of the scope of the present disclosure, and what the applicants intend as the scope of the present disclosure, is the literal and equivalent scope of the claims set forth in the specific form in this application, including any subsequent corrections. Any express definitions herein for terms contained in a claim will govern the meaning of the terms used in the claim. In addition, when we use the term "further including" in the foregoing description or in the following claims, this phrase may be followed by additional steps or entities, or sub-steps / sub-entities of the aforementioned steps or entities.

Claims

1. A method for generating one or more time series forecasts, comprising: Receiving, by a multilayer perceptron (MLP), first type of external data, wherein the first type of external data comprises time-invariant features of an object; processing, by the MLP, the first type of external data to generate an MLP output; receiving, by a recurrent neural network (RNN) unit, at least a portion of the MLP output and a second type of external data, wherein the second type of external data comprises drug dosage data, the drug dosage data representing, for each time point in a sequence of time points, a drug dosage level administered to the subject at the time point; processing, by the RNN unit, at least a portion of the MLP output and a second type of external data to generate an RNN output; as well as One or more time series predictions are generated based at least in part on the RNN output and the MLP output, wherein the one or more time series predictions include predicted concentration values ​​of the drug in plasma as a function of time.

2. The method of claim 1 , further comprising combining the MLP output with the RNN output to generate a residual output, and wherein the one or more time series forecasts are generated based at least in part on the residual output.

3. The method according to claim 1 or 2, wherein the RNN unit comprises a long short-term memory RNN unit.

4. The method of claim 1 or 2, wherein the RNN unit comprises a conventional RNN unit.

5. The method according to claim 1 or 2, wherein the RNN unit comprises a gated recurrent unit.

6. The method of claim 1 or 2, wherein the MLP comprises an input layer, at least one hidden layer, and an output layer.

7. The method according to claim 1 or 2, wherein the RNN unit comprises at least one RNN hidden layer.

8. The method according to claim 1 or 2, wherein the time-invariant feature of the object comprises an age feature or a gender feature, or comprises both an age feature and a gender feature.

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