Method for validating the predictions of a supervised model for multivariate quantative analysis of spectral data

Abstract

The invention relates to a computer-implemented machine-learning method for a multi-output prediction model (231) configured to jointly determine, on the basis of a set of spectral data characteristic of a sample, at least one primary prediction (251) of at least a first physical quantity characterising a given species in the sample and at least one secondary prediction (252) of at least a second physical quantity characterising this species, the multi-output prediction model being trained on the basis of a set of annotated spectral data (210).

Description

DESCRIPTION Title of the invention: Method for validating the predictions of a supervised model for multivariate quantitative analysis of spectral data

[0001] The invention relates to the field of quantitative analysis, for example, determining the concentration of chemical species in a sample, and supervised qualitative analysis, for example, the classification of samples, from spectral data, i.e., data exhibiting a plurality of intensity values ​​in different wavelength channels or spectral bands. The data can be both multi- or hyperspectral, where the number of spectral bands ranges from a few dozen to hundreds, and data from emission or absorption spectra of a chemical species, containing thousands of wavelength channels.

[0002] The invention relates to a novel multivariate analysis method for the quantitative analysis of chemical species contained in a sample from spectral data acquired by a spectroscopic technique. An objective of the invention concerns determining a confidence measure for the predictions of the model used for quantification, using a multioutput algorithm. More specifically, within the framework of the invention, the model provides both the primary prediction, for example, the concentration value of a species from the spectrum, and secondary outputs on tasks related to this prediction, hence the need for a multioutput system. These secondary predictions are then used to measure the confidence in the primary prediction.In other words, unlike a classical quantification approach which only predicts the main output, for example the concentration of the species of interest, the invention aims to simultaneously predict directly verifiable quantities (i.e., present in the experimental data both during training and in inference) in the experimental data and which thus make it possible to ensure the reliability of the predicted concentration.

[0003] One possible application of the invention relates to the determination of the concentration of chemical elements and an indicator of the reliability of predictions from spectral data, for example, acquired using a technique of Laser-induced plasma atomic emission spectroscopy, or "Laser-Induced Breakdown Spectroscopy" (LIBS). The invention is not limited to this particular technique; it can be applied to any type of spectroscopy technique that produces multi- or hyperspectral data, or spectral data of emission or absorption of chemical species.

[0004] Specifically, LIBS technology enables material analysis by focusing a laser beam onto the surface of a sample. The resulting plasma emission is collected by a spectrometer. The data acquired by this method are spectral data which correspond, for each focal point on the surface, to an emission spectrum comprising atomic and molecular lines characteristic of the elemental chemical composition of the sample. The intensity of these lines increases non-trivially with the concentration of the chemical elements present in the sample. Calibration is performed using several standards, i.e., samples with previously known concentrations of the species, to obtain a model that links the spectral signatures to the concentration of the species.This model can then be used to predict the unknown concentration of a species from a spectrum. Once the model is defined, methods exist for defining a measure of the uncertainty around the predictions made by the model (for example, confidence intervals). However, assessing the nature of uncertainties during the inference phase is complicated: it may be impossible or very difficult to determine whether the uncertainties are entirely due to statistical fluctuations, or whether the standards used to define the quantitative model are truly representative of the samples to be measured. Furthermore, without specific weighting of the data, calibration is characterized by relative uncertainties that increase as the concentration of the species in the standards decreases, up to the limit of detection. In fact, a level of 100% relative uncertainty is sometimes used as the definition of the limit of detection.In general, the limitations of the LIBS technique are typical of any spectroscopy technique: validation of the reliability of predictions is always problematic and relative uncertainties close to the limit of detection are by definition significant.

[0005] The invention aims to overcome these limitations by proposing: • A multivariate, multioutput quantification model to obtain both predictions of species concentrations and values ​​usable for determining their confidence. To this end, the invention introduces a technique for validating the predictions of quantitative models and for establishing a confidence measure for the predictions or for identifying the presence of anomalies (i.e., predictions that do not have a good level of confidence). • A multivariate analysis model that reduces uncertainties in determining species concentration to obtain more reliable and accurate measurements within the scope of the invention.

[0006] The invention aims to solve problems related to determining species concentration from spectral data that can be produced by LIBS spectroscopy or other spectroscopic methods (e.g., multi- or hyperspectral imaging). Generally, this type of data is characterized by spectra specific to the species present in a sample. Quantitative analysis of the spectral signatures (e.g., using the intensity of the emission or absorption lines of chemical elements) ultimately allows the species concentration to be determined. In this context, several problems can arise.

[0007] Conventional calibration methods predict the concentration of a species in a sample. Since the model is defined using known standards, there is no way to verify that the standards used to define the model represent the samples to be measured, even though this is necessarily an assumption to be made for using the model. In other words, it is impossible to verify that the samples to be measured are outside the training distribution, and consequently, to verify the generalization of the learning model. For example, the experimental conditions of a measurement when using the model may not correspond to the experimental conditions during model training because various external factors can occur related to the instrumentation, environmental conditions, or the sample itself.

[0008] The trained model always provides a prediction based on a measurement, without verifying that the data used for training is actually representative of real-world data. Therefore, there is a need for a tool to verify the reliability of predictions when conditions The conditions of use of the model vary slightly in relation to the training conditions or, conversely, in order to ensure that the conditions of use of the model have not changed.

[0009] Currently, the quantification of chemical species from spectral data is carried out using various univariate methods, which partially take into account the information contained in the spectra, or multivariate methods, which fully or almost fully exploit the content of the spectra. An example of such methods is given in reference

[0001] . Among all the variables available in a spectrum (wavelength channels or spectral bands), univariate methods use the information contained in one variable, generally the intensity of an emission line (or the sum of the intensities of neighboring channels) at a given wavelength, or of a spectral band, associated with the species to be analyzed.This information can then be used to obtain a calibration function (e.g., a straight line) that links the concentration of the species in question to the signal intensity for each of the standards, for which the concentration of the species is known. Mathematically, this procedure defines a relationship between concentration and spectral intensity. The calibration function can then be used to obtain predictions of the concentration of a species in an unknown sample by inverting this relationship, for example, by means of an interpolation such as described in reference [2].

[0010] Other multivariate methods have also been studied, notably using algorithms based on principal component analysis and multilinear regression (see reference [3]). Neural networks (described in [4]) have already been introduced in LIBS spectroscopy, either by using the intensity of certain lines selected a priori (as proposed in [5]), or by coupling principal component analysis and neural networks for multioutput regression (as proposed in [6]), or through the exploitation of information contained in time-resolved spectra (as proposed in [7]). The result of the analysis is always the prediction of the concentration of a species (or several species in [6]) as a function of several variables (hence the expression "multivariate analysis").

[0011] In recent years, deep learning techniques, given their high extrapolation capabilities, have become relevant techniques. This is also true in the case of sample classification (see, for example, [8], [9]): these analyses use high-performance algorithms (such as convolutional neural networks) to predict the category of chemical species contained in the samples. Although the architectures achieve good classification results, the confidence level of the predictions cannot be directly established by the model. As the authors of references

[0010] ,

[0011] point out, classical measures such as the mean squared error can be very misleading depending on the concentration level: the authors therefore suggest using different measures for each data subpopulation to better assess the model's performance. Other approaches have also been proposed to verify the robustness of a model, such as randomizing the model's reference values ​​in

[0012] : the authors present a technique to test whether a given prediction of the model is obtained by chance.

[0012] In general, known analyses focus on predicting a single variable (concentration) from input data of different dimensions [5], [7]. However, there are works implementing multi-output models, for example for the simultaneous prediction of the concentrations of several chemical elements using the PLS2 technique in

[0013] The first example of multioutput regression using neural networks was presented in [6]. These multioutput algorithms were used to obtain more information at the same time (notably the concentrations of several elements instead of one), while using the same input data.

[0013] However, state-of-the-art techniques do not allow for the determination of a reliability indicator for the concentration predictions provided by the different proposed learning models.

[0014] Unlike state-of-the-art solutions, the invention deals with the validation of predictions, rather than that of the model itself. The invention relates to a technique for associating a confidence measure with predictions using information available at any given time, even in unknown data, and thus directly comparing them to a ground truth value. In the invention, this is achieved through the introduction of multi-output models, and in particular through the introduction of deep learning architectures capable of efficiently processing the information contained in the data.

[0015] The invention relates to a method for validating predictions from a multi-output model. That is, the secondary outputs are experimentally measurable to allow for the evaluation of the relevance of the main output, assumed to be unknown during the inference.

[0016] The proposed invention includes an additional step compared to prior art methods. Multi-output algorithms are used to predict secondary outputs that are verifiable in experimental data, thus ensuring a degree of confidence in the predictions. This is not possible when only the concentration (or concentrations) of the chemical species is predicted.

[0017] The invention proposes using trained algorithms to predict both the concentration of a species from spectral data and to provide secondary outputs predicting additional quantities, such as the emission or absorption intensity of one or more spectral lines or bands characteristic of the analyzed species. This additional data must be measurable and experimentally verifiable during inference. Furthermore, the prediction of these values ​​must be sufficiently complex for the model, relative to the main prediction. That is, the prediction must be performed on a non-trivial task (whose complexity is comparable to that of the main prediction) using the input data to avoid imbalance during the learning process. For example, it is possible to use the intensity of spectral lines or bands integrated on channels of neighboring wavelengths.Conversely, it is not recommended to simply use the intensity of spectral lines, as this would be a trivial task to solve (it is merely a component of the input data). This type of information provides additional insights during the inference phase (hence the use of multi-output algorithms) that can be related to the actual data.

[0018] The invention makes it possible to provide, for any concentration prediction, a reliability indicator of the prediction which makes it possible, for example, to discard certain measurements subject to randomness which will make the prediction provided by the model on these measurements unreliable.

[0019] The invention relates to a computer-implemented method for the automatic learning of a configured multi-output prediction model for jointly determine, from a set of spectral data characteristic of a sample, at least one primary prediction of at least one first physical quantity characterizing a given species in the sample and at least one secondary prediction of at least one second physical quantity characterizing said species, the multioutput prediction model being trained from a set of annotated spectral data.

[0020] According to a particular aspect of the invention, the multi-output prediction model is a multi-task neural network and is implemented by means of a first common learning engine configured to extract from spectral data sets received as input, representations common to the different tasks to be solved and several learning engines specific to each task to be solved, each receiving as input said common representations and delivering as output a prediction corresponding to the task to be solved.

[0021] According to one particular aspect of the invention, the common learning engine is a convolutional neural network and the specific neural networks are convolutional neural networks supplemented by fully connected neural layers.

[0022] According to a particular aspect of the invention, said species is a chemical species, the primary prediction is a concentration value of the chemical species and the secondary prediction is an intensity value of a spectral line for at least one given wavelength or at least a band of wavelengths of a given width.

[0023] The invention also relates to a computer-implemented prediction model obtained according to the machine learning process according to the invention.

[0024] The invention further relates to a computer-implemented method for the quantitative analysis of spectral data, comprising the implementation of the prediction model according to the invention to determine, from a spectrum measured on a sample, at least one primary prediction of at least one first physical quantity characterizing a given species in the sample and at least one secondary prediction of at least one second physical quantity characterizing said species, the method further comprising a step of calculating a reliability indicator of the at least one primary prediction from an indicator of the difference between at least one secondary prediction and a value of the second corresponding physical quantity measured on the spectrum.

[0025] According to a particular aspect of the invention, the reliability indicator is equal to the relative error between the intensity value predicted via the implementation of the prediction model and the corresponding intensity value measured on the spectrum.

[0026] According to a particular aspect of the invention, the reliability indicator is equal to the absolute value of the difference between the intensity value predicted via the implementation of the prediction model and the corresponding intensity value measured on the spectrum divided by the standard deviation of this difference.

[0027] In one embodiment, the quantitative analysis method according to the invention further includes the implementation of a classification model configured to classify predictions of chemical species concentration into two classes corresponding to normal values ​​and anomalies, from predictions of spectral line intensity values ​​or reliability indicators.

[0028] According to one particular aspect of the invention, the measured spectrum is acquired by means of a laser-induced plasma atomic emission spectroscopy method.

[0029] The invention also relates to a computer program comprising instructions for the execution of a process according to the invention, when the program is executed by a processor, and to a processor-readable recording medium on which is recorded a program comprising instructions for the execution of a process according to the invention, when the program is executed by a processor.

[0030] Other features and advantages of the present invention will become more apparent from the following description in relation to the following attached drawings.

[0031] [Fig. 1] represents an example of spectral data characterizing a sample containing different chemical species,

[0032] [Fig. 2] represents a diagram illustrating the learning and use of a multi-output prediction model according to the invention,

[0033] [Fig. 3] represents a diagram of an example implementation of the prediction model according to the invention using one or more convolutional neural networks,

[0034] [Fig. 4] represents an example table of results from learning and analysis of secondary outputs.

[0035] The following description of the invention is made in the context of using LIBS technology, but the invention is not limited to this technique and applies more generally to any type of spectral, multi-spectral or hyper-spectral data.

[0036] LIBS technology enables material analysis through laser ablation and spectroscopy. The data acquired via this technique are spectral data which correspond, for each point in a zone, to an emission spectrum comprising atomic and molecular lines characteristic of the elemental chemical composition of the sample.

[0037] LIBS spectral data is obtained by focusing a laser beam onto a point on a surface to be analyzed. The plasma emission resulting from this focusing is collected and processed spectroscopically to obtain a spectrum of atomic lines (or molecular bands) of emission. The process is repeated for each point in the area to be analyzed.

[0038] Figure 1 illustrates an example of an atomic line spectrum obtained for a sample with a specific chemical composition. Figure 1 shows the spectral signatures of certain chemical elements (Ca, Al) that correspond to atomic lines in specific wavelength channels.

[0039] An objective of the invention is to determine a prediction model capable of estimating a concentration of a chemical element from an automatic analysis of a spectrum such as that in Figure 1 and to further provide an indicator of the reliability of the estimate provided.

[0040] Figure 2 represents, in a diagram, a method of learning and using a prediction model according to the invention.

[0041] The method consists, in a learning phase, of determining a prediction model 231 configured to determine, from spectra measured on given samples, a concentration of one or more chemical species on the one hand and a prediction of the intensity of one or more atomic lines (or molecular bands) in the spectrum on the other hand.

[0042] The method then consists, in a usage phase, of using the trained model to determine these predictions on new measured spectral data. The secondary outputs of the model are used to determine an indicator of the reliability of the predictions.

[0043] More specifically, during the learning phase, the method uses spectral input data in the form of several sets of spectra obtained by LIBS spectroscopy to characterize a given sample. The spectral data is labeled, meaning that, for example in the case of quantitative analysis, the concentrations of the different chemical elements to be quantified in the sample are known.

[0044] In other words, input data 210 consists of a set of pairs, each associating a spectrum with a concentration of one or more chemical elements in a sample of a given type. A sample is characterized, for example, by a type of material and a concentration of certain chemical elements in that material.

[0045] The input data 210 are separated into a first subset of training data 221 and a second subset of evaluation data 222. The model 231 is trained from the training data 221 and then it is optimized on the evaluation data 222 during an optimization cycle 232 to determine the best hyperparameters of the model 231.

[0046] The choice of the percentage of achievements used for training 221 can depend on the computing resources and the type of data to maximize the learning capacity of the architectures. For example, for a dataset containing 100,000 achievements, typically 80% can be used for training, but for datasets with millions of achievements, the percentage can increase, unless the computing resources do not allow it. The training data 221 is used directly for the calculation of the model parameters, while evaluation data 222 are used to evaluate predictions and optimize model 231.

[0047] The prediction model 231 is a multivariate and multioutput statistical model. It receives as input the entire spectra as input data and is trained to predict on the one hand a first set of primary outputs 251 corresponding to one or more predictions of concentration of one or more chemical species and on the other hand a second set of secondary outputs 252 corresponding to one or more predictions of intensity values ​​of atomic lines in certain wavelength ranges.

[0048] Once the model 231 has been trained, it can be applied to a new set of spectral data 240. The first set of predictions 251 is used to determine the concentrations of chemical species in the sample on which the input spectrum 240 was measured. The second set of predictions 252 is processed to determine a confidence measure of the first predictions 251.

[0049] The confidence measure is based on the interpretation in terms of probability (for example, using the probability distribution of a given estimator, presented below) or relative error of the predictions of the secondary outputs 252 of the model 231. These outputs must predict quantities, related to the species concentration prediction, present in the unknown real data 240, so that a comparison between real and predicted values ​​allows us to quantify the reliability of the learning and the predictions. Since the secondary outputs 252 were trained from the same representation of the input data 210, the secondary predictions 252 are related to the species concentration predictions 251 and share at least a subset of the model weights (so-called "hard parameter sharing" implementations).We can then assume that a reliable result on secondary outputs can lead to equally reliable predictions on concentration, i.e. that the generalization capacity of the model for the main output and secondary outputs is comparable.

[0050] The input data 210 used for model training are representative of the standard samples used to define the model: several spectra can represent the same standard. This data can be Preprocessed to reduce experimental fluctuations in spectral intensity values. For example, in one embodiment of the invention, each spectrum can be normalized by the intensity of a given line or band, or preprocessed by a standard normal variation (SNV) method or any other preprocessing method. In another embodiment, for each standard, the average spectral intensity value of the spectrum at a given wavelength can be used to determine outliers. For example, before defining the model, spectra whose intensity value at a given wavelength falls outside an arbitrary interval (e.g., outside the 5th and 95th percentiles, or the 1st and 99th percentiles) can be rejected. The interval depends on the measurement conditions and the number of realizations for each standard: if this number is high, a larger interval can be chosen (e.g., the 1st and 99th percentiles).In another embodiment, these two types of preprocessing can be combined. The real data used during the model application phase must be preprocessed in the same way as the input data, but it is possible to keep the outliers in the real data unknown. Indeed, if the trained model has a high generalization capacity, the outliers will be correctly handled during the inference phase. The goal is to learn the prediction task from a reliable representation of the standard: a good model must be able to extrapolate the necessary information in case the samples have defects.

[0051] The model can be evaluated using evaluation data 222 by directly using each spectrum as input data. The average predictions can then be calculated, and a deviation associated with the predictions can be used to better assess the algorithm's performance (and to train the algorithm on more complex cases where noise can produce significant differences between spectra, even if they come from the same standard).

[0052] In one embodiment of the invention, to reduce the impact of noise during the inference phase, the average spectrum of the real data 240 can be calculated beforehand and used as input data, representative of the sample.

[0053] In one embodiment of the invention, the primary outputs 251 are composed of the concentrations of the analyzed chemical species. The outputs The secondary outputs of the model contain the intensities of emission (or absorption) lines (or molecular bands) associated with the same chemical species in the case of spectral data, or the intensity measured in a spectral band in the case of multi- or hyperspectral data. In univariate models, the intensities of spectral lines or bands are used to predict concentration. Thus, including these two elements in the model's secondary outputs allows for secondary predictions corresponding to physical quantities related to the concentrations of chemical species.

[0054] In one embodiment of the invention, the quantitative analysis method includes a step of calculating a reliability indicator for the primary outputs of the model from the secondary outputs of the model. For example, the reliability indicator corresponds to a measure of the difference between the predicted intensity at the model output and the actual intensity directly measured on the input data. For example, the Student's t-value of the difference between the two values ​​can be calculated using the formula t = | / pré said > -éiiel / 0- , Or / prédite is the average intensity 252 of the sample predicted by model 231, I rée u eis the actual average intensity measured on the input data 240 and is the standard deviation of the difference (that is, the square root of the quadratic sum of the differences between the predicted and actual intensities). Finally, one can choose the confidence level as is customary for statistical analyses (e.g., 95% or 99%) to determine a threshold ti imi you, en function of the number of realizations for each sample (degrees of freedom). If the prediction / prédite leads to a value t > t limite From this, we deduce that the prediction of concentration 251 is biased, which allows us to reject this prediction based on a probability interpretation (that is, we reject the hypothesis that the difference between the prediction and the actual value is solely due to statistical fluctuations). If the prediction pr edit leads to a value t < t limiteThe available evidence does not allow us to reject prediction 251; therefore, the concentration prediction, linked to the intensity prediction, can be accepted with a level of confidence quantifiable by ti imi you-

[0055] As an alternative, we can use a simple threshold on the relative error between the true value of the intensity and its predicted value r - | / prédite - / rée n e | / eeie : the values Values ​​lower than the chosen value cannot be rejected, as their distance from the true value is primarily due to statistical fluctuations. This estimator is independent of the standard deviation of the emission intensity and can be used as a first statistical test, directly applied to the intensity values: if the prediction fails this test, then we can safely reject it, as the error is too large. The t-test (Student's t-test) can then be used as a refinement of the procedure, as it also depends on the variance of the data.

[0056] The invention thus proposes a method based on a multi-output machine learning algorithm that allows the use of information explicitly contained in the experimental data (the intensities of the emission lines in the spectrum), and therefore verifiable (by direct measurement on the spectrum), to obtain an interpretation of concentration predictions in terms of probability. The invention also proposes a method to quantitatively characterize the confidence of these predictions using the error in the secondary outputs. In particular, these predictions must have common elements with verifiable elements in the actual data to allow for comparison. The rejection (or non-rejection) of the results can then be performed using statistical tests.

[0057] In one embodiment of the invention, since the confidence level of the predictions is quantitative, the secondary predictions or the results of statistical tests can be coupled to a classification algorithm for identifying anomalies in the analyzed samples. That is, the difference between the predicted and actual values ​​of the secondary outputs can be used as input to a trained classification algorithm to recognize normal values ​​and manufacturing, compositional, or measurement anomalies. In another embodiment, an arbitrary threshold on the t-values ​​or relative errors calculated from the predictions can be used directly to determine the presence of an anomaly.

[0058] In one embodiment of the invention, the prediction model 231 may be, for example, a multilinear model (such as the PLS2 model described in reference

[0013] ), or a decision tree (or its ensemble learning variants such as random forests or gradient boosting), or a support vector machine model. The fundamental point of the model is the possibility to use a common representation of the input data to obtain multi-output predictions simultaneously, that is, an approximation of the composition of the function f ° g, where g ∈ IR W -> A c [R L and / : A -> IR MN is the dimension of the spectra, L is the dimension of the common representation, and M is the number of predictions output by the model, such that M > 2, using the same set of parameters for the model definition. In this way, the model first calculates a new representation of the input data (the spectra), which can then be used to generate the predictions.

[0059] In general, to train model 231, the definition of a learning function (or loss function) £ t P our ' a sort i e i of the model is needed (y^ eüesand ypredites represent the actual and predicted values ​​of output i): this allows us to define the training objective and measure the difference between the predicted and actual values ​​(in supervised learning, the actual values ​​are known during training). Thus, there are loss functions typically dedicated to regression learning, unlike loss functions typically used for classification tasks. In various embodiments of the invention, a mean squared error function or a mean absolute error function can be used. In another embodiment of the invention, these functions can be combined in a so-called "Huber loss" function as described in reference

[0014] , defined by:

[0061] where 8 is one of the hyperparameters to be optimized during the 232 optimization cycle of the model and 0 is the Heaviside function which takes the value 1 for all strictly positive real numbers and the value 0 for strictly negative real numbers. This function allows us to directly take into account the problems related to outliers present in the datasets.

[0062] Once the loss function chosen for output i of the model, the overall loss function of the model is defined as a linear combination of the loss functions specific to each output: many of their real ones specific to each release, is the set of predictions of the model outputs, and fl = { > £ G IR}ie{i / vj is the set of coefficients of the linear combination of the loss functions. The coefficients ÛJ £ represent hyperparameters of model 231.

[0063] In another embodiment of the invention, model 231 is implemented using one or more neural networks. An example of the architecture of model 231 is shown in Figure 3.

[0064] In one embodiment, the neural networks constituting the model 231 are convolutional neural networks. A convolutional neural network is implemented via a set of convolutions by vectors extending in the direction of the wavelength channels of the spectra. The input data are scanned using several convolution filters to obtain both the primary predictions 251 and the secondary predictions 252 from a multioutput model.

[0065] These neural networks can be deep, with multiple hidden layers, connecting convolution and activation operations, with their trainable weights. The advantage of this type of algorithm is the direct use of information contained in spectra: by using a convolution operation, one can maintain the relationships between channels of neighboring wavelengths and utilize the physical information contained in the profiles of spectral lines (or spectral bands), such as emission or absorption intensity and profile width.More generally, other types of neural network architectures, such as fully connected neural networks (based on multilayer perceptrons as described in

[0016] ) or graph networks as described in

[0017] , can also be used: a sufficient condition of the invention is the ability to form multi-output architectures, without specific restrictions on the type of neural network.

[0066] The example in Figure 3 represents a multitask network (as described in reference

[0020] ). The difference between a multitask network and a multioutput network lies in the way data representations are handled in the hidden layers: a multioutput network uses a common representation without further transformations, but a multitask network allows the use of a common representation followed by specialized branches for specific tasks. In this sense, a multitask network is a multioutput network, but the reverse is not true. Using a multitask architecture helps to resolve many problems related to overfitting training data and to limit the impact of outliers on predictions (as discussed, for example, in reference

[0018] ).

[0067] The algorithms used can be based on multitasking deep convolutional neural networks. This gives the models the ability to directly analyze spectra, formulating a new common representation of the data, and to predict with high accuracy either the concentrations of species of interest or, for example, the intensity of spectral emissions associated with those species. These predictions can then be interpreted by probability models by studying the difference between the predicted and actual values.

[0068] The input data 310 of the model have already been described: they consist of spectra acquired by a spectroscopic technique, possibly preprocessed. The first block of the model 320 is represented by a neural network comprising one-dimensional convolutional layers. This first block is tasked with learning a common representation of the spectra using the same set of weights and parameters ("hard parameter sharing"). Several examples of implementations of multitasking neural networks are given in reference

[0019] . It aims to transform the input data into a representation capable of providing predictions for all tasks simultaneously.

[0069] The outputs / tasks of model 341-343, including the concentrations of the analyzed species and the values ​​used for confidence determination, are calculated using other specific convolutional networks 331-333: each network allows for further transformations from the common representation to yield a specific result. For example, the The model calculates the secondary outputs (the intensities of the spectral lines present in the spectra) starting from this common representation and then processing it in specific branches. Thus, the model does not simply "read" the intensity from the spectra, but is required to first find a suitable representation of the input data and then process that information. This type of network offers a significant improvement over traditional networks.

[0070] The 331-333 convolutional neural networks take as input a vector of common features extracted from the input data via the first 320 neural network, and produce as output a prediction in the form of a scalar. To achieve this, each 331-333 convolutional neural network includes a final layer that is fully connected to an output.

[0071] An example of a possible architecture for the multitasking model in Figure 3 is defined by: - a first neural network 320 formed by 3 convolutional layers with respectively: i. 64, 40 and 16 filters, ii. kernel size: 5, 3 and 2 wavelength channels, iii. step size: 3, 2 and 1 wavelength channels, - neural networks to solve specific tasks 331 - 333 having the same hyperparameters as the first neural network 320 and supplemented by two fully connected layers of 16 and 1 neurons respectively (each network 331 - 333 predicts a real number).

[0072] The activation function after each hidden layer is, for example, of the "LeakyReLU" type (with a slope of 0.03). The learning rate is, for example, set to 10 -3 .

[0073] Figure 4 presents a table showing the results of the calibration of iron (Fe) concentration in a nickel (Ni) matrix and a zirconium (Zr) matrix. Twenty-five laser shots were recorded for each sample, and each spectrum is formed by 68,000 wavelength channels. The secondary outputs are the intensity values ​​of the Fe emission lines at 373.49 nm, 358.12 nm, 373.71 nm, 374.56 nm, 382.04 nm, 385.99 nm, 404.58 nm, and 438.35 nm. The training consists solely of spectra of Ni standards (the results are given on an independent test set). As shown in the table, the multivariate architecture (MVA), based on multitask learning, is capable of providing more accurate predictions than the classical univariate method (UVA) on matrices of the same nature as those used for training. The multitask architecture is also capable of providing a measure of the reliability of the predictions on the Ni matrices by using a confidence measure on the predicted intensities for the emission lines (in this case r). limite = t a v= 2.485, where the confidence level is a = 0.99 and the degrees of freedom are v = 25). The table also shows the generalization capabilities on a Zr matrix, which differs in nature from the training samples: the neural network is able to significantly reduce the error in the extrapolation regime. However, the multitasking architecture allows us to measure the reliability of the predictions: the relative errors of the emission line intensities (and the t-values) in the Zr samples are indeed very high. In this case, the Zr matrix was recognized as anomalous compared to the training distribution.

[0074] The invention allows for the quantification of confidence in predicted concentrations using probability models based on a set of predictions from a multioutput model. The model can predict both the concentration of species and other quantities (e.g., the intensity of emission lines of a chemical species). This provides access to both unknown quantities (e.g., species concentrations) and secondary quantities that can be directly verified in spectra, and which are used to determine the confidence level of the quantitative analysis.

[0075] The invention makes it possible to reduce uncertainties by using efficient algorithms capable of directly and fully automatically processing the spectral signatures of the species contained in the entire spectra.

[0076] The steps of the invention can be implemented as a computer program comprising instructions for its execution. The computer program can be stored on a storage medium readable by a processor.

[0077] The reference to a computer program that, when executed, performs any of the functions described above, is not limited to an application program running on a single host computer. Rather, the terms computer program and software are used here in a general sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instruction) that can be used to program one or more processors to implement aspects of the techniques described herein. These computing means or resources may, in particular, be distributed ("cloud computing"), possibly using peer-to-peer technologies.The software code can be executed on any suitable processor (e.g., a microprocessor) or processor core, or a set of processors, whether located in a single computing device or distributed across multiple computing devices (e.g., as potentially accessible within the device's environment). The executable code for each program, enabling the programmable device to implement the processes according to the invention, can be stored, for example, on the hard drive or in read-only memory. Generally, the program(s) can be loaded into one of the device's storage means before being executed. The central processing unit can command and direct the execution of the instructions or portions of software code of the program(s) according to the invention, instructions which are stored on the hard drive or in read-only memory, or in the other aforementioned storage elements. References

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Claims

CLAIMS A computer-implemented method for machine learning a multioutput prediction model (231) configured to jointly determine, from a set of spectral data characteristic of a sample, at least one primary prediction (251) of at least one first physical quantity characterizing a given species in the sample and at least one secondary prediction (252) of at least one second physical quantity characterizing said species, the multioutput prediction model being trained from a set of annotated spectral data (210).A machine learning method according to claim 1, wherein the multi-output prediction model is a multi-task neural network and is implemented by means of a first common learning engine (320) configured to extract common representations from spectral datasets received as input, and several task-specific learning engines (331, 332, 333) for each task, each receiving said common representations as input and delivering as output a prediction (341, 342, 343) corresponding to the task to be solved. A machine learning method according to claim 2, wherein the common learning engine (320) is a convolutional neural network and the task-specific neural networks (331, 332, 333) are convolutional neural networks supplemented by fully connected neural layers.A machine learning method according to any one of the preceding claims, wherein said species is a chemical species, the primary prediction is a concentration value of the chemical species, and the secondary prediction is an intensity value of a spectral line for at least one given wavelength or at least a band of wavelengths of a given width. A computer-implemented method for the quantitative analysis of spectral data comprising the implementation of a prediction model (231). trained by means of the machine learning method according to any one of the preceding claims to determine, from a spectrum (240) measured on a sample, at least one primary prediction (251) of at least one first physical quantity characterizing a given species in the sample and at least one secondary prediction (252) of at least one second physical quantity characterizing said species, the method further comprising a step of calculating a reliability indicator of the at least one primary prediction from an indicator of the difference between at least one secondary prediction and a value of the corresponding second physical quantity measured on the spectrum. Quantitative analysis method according to claim 5 wherein the reliability indicator is equal to the relative error between the intensity value predicted via the implementation of the prediction model and the corresponding intensity value measured on the spectrum.A quantitative analysis method according to claim 5, wherein the reliability indicator is equal to the absolute difference between the intensity value predicted via the implementation of the prediction model and the corresponding intensity value measured on the spectrum, divided by the standard deviation of this difference. A quantitative analysis method according to any one of claims 5 to 6. 7 further comprising the implementation of a classification model configured to classify predictions of chemical species concentration into two classes corresponding to normal values ​​and anomalies, based on predictions of spectral line intensity values ​​or reliability indicators. Quantitative analysis method according to any one of claims 5 to 8 in which the measured spectrum is acquired by means of a laser-induced plasma atomic emission spectroscopy method. Computer program comprising instructions for carrying out a method according to any one of the preceding claims, when the program is executed by a processor. Processor-readable recording medium on which is recorded a program containing instructions for the execution of a process according to any one of claims 1 to 9, when the program is executed by a processor.

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