WO2010060746A2 - Method and device for the automatic analysis of models - Google Patents

Abstract

The invention relates to a method and a device for the automatic analysis of a non-linear model for predicting the properties of an object which is a priori not characterized. According to the method, a) the non-linear model is elaborated for training objects based on a mechanical learning method, especially a kernel-based learning method, in such a manner that it allows a statement regarding at least one property for at least one object, b) at least one measure is automatically determined by means of an analytical element using the representer theorem, said measure indicating which training object or which training objects that have become part of the non-linear model have the strongest influence on the predictions of the non-linear model, and c) a prioritized data set is automatically produced in which the measures of the influencing factors are put in the order of a predetermined condition.

Description

Method and device for automatic analysis of models

In the following, a method having the features of claim 1 and a device having the features of claim 14 are claimed.

In many areas of technology and business, nonlinear models of real data are used to make predictions. These models are so complex that they can hardly be investigated by analytical methods. This means that a user of a non-linear model is confronted with a kind of black-box, where he does not know the factors that are essential for a prediction in a particular case and that have found their way into the model.

It is therefore an object to develop methods and devices which enable an automatic analysis of such models and the results of this analysis for further use.

This object is achieved by a method having the features of claim 1 and an apparatus having the features of claim 14.

In the following, embodiments of methods and devices will be described in connection with figures. Show

1 is a flowchart of an embodiment of a method;

Fig. 2 is a schematic representation of training and model generation and analysis; Fig. 3 is an illustration of the effect of reducing the core width on the ability to generalize;

Fig. 4 is an illustration of an example of toxic and non-toxic compounds;

5 is a flow chart of an embodiment of the invention

Method for automatic determination of an explanatory model;

Fig. 6 shows an example of the use of the method;

Fig. 7 shows an example of a use of the method in connection with two test molecules;

Tab. 1 shows an example calculation of the percentage that each training molecule contributes to the prediction for test molecule 1;

Tab. 2 shows an example calculation for the percentage that each training molecule contributes to the prediction for test molecule 2.

The methods and apparatus described below use nonlinear models that are automatically extracted from data using machine learning techniques.

In the context of this description, machine learning is understood to mean the basically known supervised machine learning. In this case, an automated machine learning process recognizes laws and correlations in a training set that allow statements about properties of a new object. One possible example, discussed below, is the automatic generation and analysis of a non-linear model for predicting the toxicity of chemical molecules.

By a prediction is meant an estimate indicating for each chemical molecule its toxicity in the form of a number. If this number exceeds a threshold determined in the training process, the prediction can be interpreted as "toxic", otherwise the prediction is "non-toxic". Gauss's processes can be trained to interpret the output directly as a probability, e.g. "72 of a hundred molecules with these characteristics are toxic".

Hereinafter, under feature, a descriptive quantity, e.g. calculated from the structural formula of a molecule, e.g. its size, weight, surface, the number of certain functional groups in the molecule, etc. understood in chemical computer science, these features are synonymously referred to as descriptors.

As will be described later, such a nonlinear model is not only created and used for prediction, but it is also automatically analyzed to determine at least one major influential factor (eg, the main reason why the model predicts toxicity) and further use of that data enable.

Although reference is repeatedly made below to the prediction and analysis of toxicity, those skilled in the art will recognize that the methods and apparatus are also suitable for other data, models, and articles, such as the model-based control of a chemical plant. Also examples are given. In any case, the resulting models have the special feature of providing additional information that facilitates the user's understanding at an interface, so that they can subsequently be visualized, for example, in the form of a ranking list or in the form of a graphic.

When reference is made to a model below, this may be e.g. a computer program, i. a formalized sequence of logical commands. A model can also be represented by mathematical relationships and / or tables of values.

Fig. 1 shows a basic form of a method by which a non-linear model (e.g., a computer program, a look-up table, a mathematical model, etc.) can be created and automatically analyzed. The model may e.g. as a non-linear model or as part of a machine learning procedure. For the example according to FIG. 1, the latter case is assumed.

The aim is to obtain a model with which properties (for example toxicity, control behavior) of an a priori uncharacterized object (eg molecule, chemical plant) can be predicted and at the same time the influencing variables of the model are determined. Property will hereinafter be understood as meaning in each case a measured or measurable property of a chemical compound, e.g. their water solubility or toxicity, understood.

In the first method step 100, the non-linear model is automatically formed by a machine learning method from a multiplicity of known training objects in such a way that at least one article has at least one statement for at least one article a property allowed.

In case of toxicity, the automatically determined non-linear model allows a binary statement, toxic - non-toxic. For the application case control behavior, this statement can be made e.g. adhering to or disobeying a determine metric or quality characteristic.

An analysis means is used in the second method step 200 to automatically determine at least one measure that indicates which exercise item or items of training that have become part of the non-linear model have the greatest impact on the non-linear model. Influence is understood here as the size of the normalized coefficient of a training object in the linear combination with which the prediction can be calculated. A quantitative example is given in connection with FIG. 7 and Tables 1 and 2.

The analysis means uses a special property of the automatically determined non-linear model to measure this measure. This measure can be determined, for example, with the aid of the representer theorem (or a mathematically equivalent formulation of the prediction function) whose core message is that the prediction of core-based models can be formulated mathematically as a linear combination, which will be explained in more detail below. The validity of the representative theorem is a well-known property of a kernel-based non-linear model, which is determined by a machine learning method.

In the third method step 300, a ranking data record is then automatically created, in which the measures are arranged according to a predetermined condition. The following describes a concrete embodiment, namely the automatic analysis of a model for the prediction of the toxicity of chemical molecules. Those skilled in the art will recognize that other properties of chemical molecules, such as water solubility, metabolic stability, binding to certain receptors, etc., can be similarly analyzed.

A special feature of the resulting models is that the predictions are comprehensible in terms of content due to the automatic quantitative evaluation of influencing variables. For this purpose, additional information is provided at an interface, so that these can be visualized in the following or used in the context of a model reduction. Optimization aids can be used for model reduction, which will be explained in more detail below.

In one embodiment, by means of a machine learning method, the relationship between the structure of the molecules and their toxicity is determined from a training set of data. As a training set for a supervised method of machine learning, the features (here the number of different functional groups or other molecular constituents) and the measured toxicity for a set of chemical molecules function. Toxicity is the property of a substance to harm an organism. The damage can affect the whole organism or one of its substructures such as organs, cells or DNA. In the following embodiment we refer to genotoxicity, measured as Arnes mutagenicity. The method is by no means limited to this measure. Alternatively, measurements such as the micronucleus test or chromosome abberation can also be used. The training is performed on a program called "ToxTrain" in the described embodiment This program involves an implementation of a supervised machine learning method, namely a Gaussian process known per se.

The result of the training is a program "ToxExplain", which contains the learned context as a model and thus can generate predictions about its toxicity for new molecules.In addition to the pure prediction, the embodiment also determines so-called explanatory components and optimization aids, which can be used over an interface eg The model can also be a stand-alone program, which can also be output as a module or plug-in for existing software in a company, or implemented in hardware form, ie on a chip.

The procedure, which will be described in detail below, automatically provides explanatory components that characterize the non-linear model, which is also generated automatically. This means that the prediction of a model for a new molecule (eg, toxicity) is largely based on a certain small number of molecules (or even parts of it, such as functional groups) in the training set. In this case, one can, for example, visualize these few important molecules or use them as the basis for an automatically generated simplified model. The presentation remains clear and it is understandable how the prediction of the model comes to pass. In known methods, it is only possible to work with the complex non-linear models, since it is not clear which parts of the model have a special influence on the predictions of the model. By the automatic Determining the explanatory components, ie the parts of the model that have a great influence on the predictions, it is possible to easily automatically obtain a reduction of the complexity of the non-linear model.

A model that can automatically identify such explanatory components is called explanatory.

By an optimization aid, an ordered list (i.e., the list elements are each given a measure of the feature) is understood to mean those features of a molecule on which the prediction of the model most depends. Thus, e.g. automatically determining variations of the molecule, e.g. less toxic than the parent molecule.

In Fig. 2, these relationships are shown. The upper part of FIG. 2 describes the training in which a training amount is examined with the aid of the program ToxTrain. This automatically generates the program ToxExplain, which not only makes predictions possible, but also has explanatory components. This is shown in the lower part of Fig. 2. The models of type ToxExplain explain their predictions and provide optimization aids and can then be further processed, e.g. for model reduction or visualization of the ranking of influencing factors.

Many properties of chemical compounds (toxicity, water solubility, metabolic stability, binding to certain receptors, etc.) are non-linearly related to certain features of their molecules. Such relationships can not be adequately described with simple linear models. With the help of machine learning methods (eg Gauss' processes, support vector machines) can be also model complex nonlinear relationships.

In the following, in particular machine learning methods are considered, which are based on core functions (synonym covariance function). The kernel function in kernel-based learning has the task of implicitly transforming the features of two objects (e.g., chemical molecules) into a very high dimensional feature space and calculating the scalar product there. Since the core function can perform non-linear transformation, by using a suitable kernel function, any linear learning methods in which the features of objects (here: molecules) appear exclusively in the form of scalar products, can be generalized such that they are used for learning non-linear relationships can be used.

Examples of core functions are the RBF core (synonyms: Radial Basisfunction Kernel, Gauss Kernel, graphkern, treekern, Squared exponential Kernel) and the polynomial kernel.

An example of a machine learning method is a Gaussian process that can be used to generate models that, in addition to predictions, also output the variance of the respective prediction. Gauss's processes were originally developed for regression of data, but can also be used for classifications.

In contrast, the support vector machine is a machine learning method that was originally developed for the classification of data, but can also be used to regression data.

Classification is the construction of a model for properties that can be expressed by categories or membership of groups. Molecules are eg "mutagenic" or "not mutagenic". This is contrasted with the regression, in which a model is constructed whose properties can be expressed by real numbers, eg the strength of the binding of a molecule to a receptor protein. Also, the toxicity can be given in the form of real numbers.

One of the central ideas is that reliable classifications can be accomplished in the training volume starting from a few objects that are important for the decision (here: molecules).

The models resulting from the kernel-based learning process can, based on various features of new molecules, generate predictions for previously unobserved or measured properties of these new molecules, i. e.g. predict their toxicity. The more observed / measured data from the past is available as a training set, the better a given relationship can be modeled and the more accurate the predictions for previously unseen molecules become. Due to their high performance, statistical learning methods of this kind are already used in many fields. However, they have a decisive disadvantage: For the user of such a model, it is generally not comprehensible how the prediction comes about in a specific individual case.

This disadvantage is, depending on the exact nature of the application, different in importance. In the development of new drugs, different phases can be distinguished. In the "lead optimization" phase, experts decide in a specific case which chemical compounds are next synthesized and tested. They make this decision on the basis of the experimental data generated so far in the project Results, relevant experimental results, their general experience and intuition and the predictions of models. Available models may contain information that is unknown to the respective expert. Complex models that are state-of-the-art would provide correct predictions in this case, but they are incomprehensible to the expert. They may even be in apparent contradiction to experimental data available to the expert. In such a case, the expert will not rely on the prediction of the model and may make an unfavorable decision.

Typical questions asked at this stage are:

1. How does this concrete prediction come about? Which of the molecules in the training set does this prediction depend on?

2. What needs to be changed on a toxic molecule to get a non-toxic molecule?

Since the otherwise very powerful statistical learning methods can not provide answers to these questions, less powerful linear models are usually used here. These are often trained by hand with small amounts of training (less than a hundred chemical compounds in a series). By series is meant a group of chemical compounds having the same basic body but differing in which functional group is present at a particular position, how long a particular side chain is, etc.

Useful information about several (possibly thousands) chemical compounds from other series can be found on this Do not infiltrate and increase the accuracy of the prediction. With this disadvantage, however, one buys the possibility of at least partially answering the two above-mentioned questions.

The embodiment described below makes it possible to provide powerful statistical learning methods with the hitherto lacking traceability and to answer the above two questions as follows:

1. The method and the device allow to identify a few molecules relevant to the respective prediction from the training amount. These are referred to below as explanatory components. In the past, attempts have been made by various research groups to estimate the reliability of predictions taking into account the amount of training. However, the previous strategies are independent of the learning algorithm and therefore not adapted to its specifics. Only the close coupling or integration of the determination of the explanatory components to the learning algorithm makes it possible to identify the molecules on which the prediction really depends.

2. The most important characteristics for the respective prediction are automatically identified with the help of the method and serve as optimization aids. This automatically determines the characteristics of each molecule whose toxicity depends the most. The most important features are determined locally, which will be explained in more detail later. Thus, the local gradients are determined, which are then used as optimization aids.

Generally, a gradient is a differential operator that can be applied to a scalar field. The term is used synonymously for the vector whose elements are the partial derivatives of a function after all of their Variables are. In the context of the present embodiment, the gradient is understood to mean a vector with the partial derivatives of the prediction of a model for a specific molecule according to its characteristics. For some kernel-based learning methods (eg for Gaussian processes), the gradients can be calculated directly analytically. For learning methods whose prediction functions do not permit analytical calculation of the gradient, the gradients are calculated using a differentiable density estimator (eg, Parzen Window) that is closely matched to the prediction function so that the gradients of the density estimator can be considered a predicted prediction function ,

In connection with Fig. 3, the fundamental relationship between the explanatory ability and

Generalisability of core-based models, i. especially described by Gauss's processes.

Generalization ability is understood here as the ability of a model to produce accurate predictions for molecules that are not included in its training set.

In the upper part of FIG. 3, the number of explanatory components is plotted as a function of the core width. Many core functions, including the RBF core, have a hyper-parameter called core-width. In the present exemplary embodiment, the kernel width controls whether predictions of a model depend in each case only on the properties of molecules which are closely adjacent to the new molecule in the feature space or whether more distant molecules are also taken into account.

In Fig. 3, the core width becomes smaller from left to right, and the number of explanatory components decreases. That is the Prediction for a new molecule relies on fewer and fewer molecules from the training set. If a prediction relies on very few (eg five) molecules, they can be visualized in a clear way. Visualization enables human experts to understand predictions and assess their reliability. A model that can provide the necessary information via an interface is called explanatory. The quantitative treatment of the explanatory ability will be described in connection with FIG.

As the number of explanatory components decreases, it is possible to reduce the complexity of the model. If the later scope of application of the model is known, or if one knows even during the creation of the model for which previously uncharacterized objects one wants to generate predictions later (so-called semi-supervised machine learning), then one can reduce the training set to just these explanatory components. This reduces the complexity of the model as well as the computational effort for creating and applying the model.

In the present embodiment, a novelty is that the kernel width learned from the Gaussian process (left vertical line) is subsequently reduced (see FIG. 5). A slightly increased mean error (i.e., degradation of the model) is accepted in order to reduce the number of explanatory components to a clear level (right vertical line). The different crosses in the curves represent different measures for the number of explanatory components or the error (median, mean etc.) and show uniform trends.

The lower part of Fig. 3 shows the relationship between the generalizability of the model and its core width. The core width is plotted with the same scale as in the upper part, ie it decreases from left to right. Generalisability is measured by the mean error the model makes in predicting new molecules. This was determined for various core widths with a test set of molecules that were not considered in the training of the model. In the left half (relatively large core width), the mean error for new molecules is small. If you reduce the core width, the mean error increases (right half).

As a test set (or test set) for a supervised machine learning process, there are a number of chemical molecules represented by appropriate features. If the generalization capability of a model is to be determined, it makes sense to use only molecules that are not contained in the training set of the model as a test set.

The optimization of the core width is part of the normal training process for Gauss' processes. However, this optimization is basically carried out with the aim of achieving the lowest possible mean errors for new molecules. This optimum is symbolized in Fig. 3 by the left vertical line.

In the present embodiment, following the optimization, the kernel width is automatically reduced (see FIG. 5) to obtain a clear number of explanatory components. As the figure shows, the ability to generalize deteriorates measurably, but not severely. This means that a compromise between the ability to generalize and the ability to explain can be achieved, ie the user can use ToxTrain to generate models from his own datasets which can be explained and nevertheless generalize relatively well.

Due to the automatic reduction of the kernel width, there is a possibility to automatically create a model reduction following a model formation. The automatic Kernweitenreduktion will be explained in more detail in connection with FIG.

As mentioned above, the present embodiment allows the influence of certain features to be determined locally.

To illustrate this, let us introduce a recent example from the drug search research. Chemical compounds whose molecules contain one or more epoxy groups are usually toxic. However, steroids are not. Steroids can contain epoxy groups and yet be non-toxic.

Fig. 4 illustrates this relationship. In this 2-dimensional projection of the space spanned by the features of the molecules, steroids (circles) and non-steroids (squares) each form a local neighborhood. The steroids are located in the lower left corner of the quadrant, the non-steroids in the upper right corner.

Epoxy-group non-steroids are usually toxic (hatched circles and squares), while steroid-containing steroids may be both toxic and non-toxic (non-hatched circles and squares).

Globally, the epoxy group is an important feature in terms of the toxicity of the particular compound. In the local neighborhood of steroids, however, this globally obtained information is misleading. This example shows that considering the local environment can be essential for generating optimization tools.

With the methods known from the prior art, operating globally (ie, on the total exercise volume), one would conclude that to avoid toxicity even with steroids, the avoidance of epoxy groups would be helpful, although there are quite a few non-toxic steroids with epoxy groups.

The globally correctly recognized trend would therefore lead to misleading optimization aids due to the locally different behavior of the steroids. Only the consideration of the local influence of various features (here: presence of an epoxy group) allows the automatic generation of targeted optimization aids by means of the present embodiment.

These optimization aids would not include the epoxy group as a criterion for toxic steroids but would instead name relevant characteristics for the particular molecule. However, for toxic non-steroids, the optimizers would in any case include the epoxy group as a toxicity-relevant feature.

Thus, with the present embodiment, it is automatically possible to measure the influence of certain features on the prediction result.

It was mentioned above that in the drug search research possibly linear models are used with small training amounts. For the specific case of steroid toxicity, the global gradient from a linear model would be meaningful if and only if it compensates for the local gradient of a complex model Model would correspond. This correspondence can be achieved by making the training amount very local from the outset. That is, if you want to make predictions for steroids, you can only use steroids as a training amount. Thus, the expert must already know in advance about the locally different behavior of different compound classes and specifically generate different local models. After all, he has to use the most appropriate model for each new molecule.

In contrast, the problem can be solved better with a program ToxTrain. All available data can be used as training amount. The resulting model ToxExplain always generates its optimization aids for each new molecule from the local gradient of the prediction according to the characteristics of the molecule. In this way, the user receives a targeted optimization help, which can be extracted from the entire available data.

In the following it is shown how the local gradients of the predictions of Gauss' process see models for new molecules according to the characteristics of these same molecules. The prediction f _new for a new molecule is calculated as follows:

I

The sum runs over all N molecules in the training amount. CC ₁ is the element i of the vector a = (K + σ ² l) ^{~ ι ■} y. In it are:

K-i, j = k (x, Xj) for the complete kernel matrix of the training set,

σ for the learned noise level, I for the identity matrix and

y _Σ for the measured toxicity of each molecule.

k ( ^x new> ^x ,) denotes the core function between the features Xn _{eur of} the new molecule and the characteristics of the respective molecule i from the training set.

Among other things, different kernel-based methods differ in how elements CC _{1 of} the weight vector are determined. The above expression for the weight vector relates to a Gaussian process, and in principle other core-based methods are also possible for implementing the method.

We choose the RBF core function (with the kernel width w)

k (x _new , _Xl ) = e - ^ - ^X ' ^{) 2} - ^W (2)

and insert them into equation (1). By deriving the resulting expression according to the characteristic j in the feature vector x _{rieu of} the new molecule, we obtain the local partial derivative:

2wΣa _r y _t ^■ (x _newj -X _1} ) -er & new- *,) ² - ™ o:

X ₁ and Xn _eu are vectors, whereby a partial derivative to the j-th component is formed.

The partial derivatives together then form the local gradient of f _neu according to the characteristics of the new molecule and form the basis for the calculation of the optimization aids by the program ToxExplain. It will be understood by those skilled in the art that the same approach can be used for other features to determine other properties than toxicity. The determination of the partial derivatives also allows the automatic determination of optimization aids for other features and thus a possibility for better model reduction. In order to carry out the model reduction, one calculates for all molecules in the respective training amount their optimization aids, ie one receives for each molecule the sensitivity after each characteristic (measured in per cent). Then, for each feature, one calculates the average amount that the sensitivity for this feature reaches on average across all molecules. After this average amount, the list of characteristics can now be sorted and thus converted into a ranking list. In the sense of a model reduction, the features can now (exclusively) be used at the head of the feature list generated in this way.

A flowchart for a run of the program ToxTrain is shown in FIG.

After the start of the program (method step 1), a data set specified by the user is first loaded. Using this data set, a Gaussian process is then trained in method step 2, ie, using a per se known machine learning algorithm, the relationship between the molecular structure of the chemical compounds contained in the data record and their toxicity is learned. Part of this training process is the internal optimization of the evidence. This is a mathematical function that is used as a criterion in various methods of machine learning to optimize parameters. In Gauss' see processes In this way, the fit of predictions and predicted variances is considered equally.

The goodness of the Fit describes how closely a model is adapted to its training amount. Unterfitten means not adapting a model closely enough, e.g. too complex to make, such as when trying to represent a nonlinear relationship through a straight line. Overfit means too tight an adaptation of the function to the training set, so that exact predictions are obtained for all molecules from the training set, but for new molecules only very inaccurate predictions are achieved (poor generalization ability).

As explained above, among other things, a value for the core width is automatically determined, which is optimal with regard to the expected generalization capability. This model is referred to below as GP _gen .

In the following process steps 4 to 9, the core width is now gradually reduced automatically until the model can be explained (see method step 7).

With this newly calculated, reduced kernel width, a model is subsequently trained on the entire input data record (method step 10). The second model is called GPfj. _t denotes. Both models, GP _gen , and GP _flt are stored (step 11). Together they form an explanatory overall model of the type ToxExplain.

The question arises as to why two Gaussian process models are being produced with different core widths. As explained above, a sufficiently small kernel size is a prerequisite for the model to be able to explain. This relationship is shown in FIG. Another important aspect in the application of the resulting models is the identification of the locally most important features. These facilitate the optimization of compounds, ie, for example, the reduction of the toxicity of an active substance by targeted modification of its molecular structure. These optimization tools are generated from local gradients of the core function of the Gauss' process model. The reduction of the kernel width to the training of the model G _flt (with the goal of the explanatory _ability ) leads to a close fit of the learned function to the training _data . As a result, the function is generally less smooth than that of the GP _gen model, and the local gradients are less useful in terms of use as optimizers. So both models are saved in order to be able to determine both good predictions and helpful optimization aids with the program ToxExplain.

In the following, the individual method steps in the flowchart of the program ToxTrain (FIG. 5) are explained in detail.

Process step 1: ToxTrain is started

Process step 2: A data record is loaded. This contains the following information for a number of chemical compounds:

• A reading for the Toxicity property

• The structural formula of the molecule

• A series of features calculated from the structural formula

(Chemical or molecular descriptors) of the molecule, ie, for example, its mass, surface area, the number of certain functional groups (such as the described in connection with FIG. 4 epoxy group) etc .. Process Step 3: Using the entire data set from process step 2, a Gaussian process model is trained. In the process, all model parameters are automatically adjusted using the gradients of the evidence function so that the evidence is maximized. This parameter estimation or model selection strategy is state of the art in machine learning and generally leads to models that generalize well.

Process Step 4: The molecules from the data set obtained in method step 2 are randomly separated t-times independently into non-overlapping sub-data sets, which are referred to later as a training or test set. It makes sense to use at this point the known per se cross-validation strategy with at least 10 repetitions.

Cross-validation methods are often used to calculate the

To estimate the generalization capability of a particular type of model that can be generated using machine learning techniques. A 5-fold repeated 3-fold cross validation means that the molecules in the dataset are randomly distributed in three equal parts (folds). Subsequently, two of these folds are used as a training set, ie on their basis a model is trained. This model is used to generate predictions for the third FoId. In the same way FoId 1 + 3, as well as 2 + 3 combined are used as training sets and the resulting models are used to generate 2 or 1 predictions for each remaining folds. Now predictions have been made for the entire dataset, using a model for each prediction that did not have the molecule in its training set. Because the concrete randomly made initial distribution of the molecules in the data set to three folds that may facilitate or complicate modeling, the entire procedure is repeated five times starting from this random distribution step. The generalization of 5-fold repeated 3-fold cross-validation (so-called 5x3 CV) to nxm CV can be done by using a larger number of folds and repeating them more often.

Process Step 5: With each of the training sets generated in method step 4, a Gaussian process is trained. However, unlike usual, no internal optimization of all parameters is made, but the core width is excluded from this optimization. Instead, the determined in step 3 (or from the 2nd run of the loop determined in step 10 reduced) core width is adopted and not further adapted.

Method Step 6: The models trained in method step 5 are now used to generate predictions for the test sets belonging to the respective training set from method step 4. That For all molecules in the respective test set, the toxicity is predicted and the mean error of these predictions is determined.

Method Step 7: For all predictions made in method step 6, the explanatory components are determined. That is, those molecules i from the respective training set are determined, which together contribute more than 80% of the respective prediction f (x _new ). The prediction is formed by means of the representer theorem, which applies to all kernel-based methods:

f (x _new) = a + ₁ c .sigma..sub.B _Jl k (x _1, x _n) A)

The running index i runs over all molecules in the training amount. The quantities a, b _± , and C ₁ are (depending on Learning algorithm) various local and global parameters. k (Xj_, x _n ) is the core function between the features of one molecule each of the training set X ₁ and the features of the new molecule x _n . The contributions to the sum in equation (4) are sorted by size, and additional contributions are added by the head of the list until the subtotal of the contributions reaches 80%.

In this method step, a measure is calculated, on the basis of which a ranking data record is automatically created. The measures of the influencing factors can then be arranged according to a predetermined condition.

Step 8: If more than 50% of the predictions from step 6 can be explained by five or less explanatory components (i.e., five or fewer tracer objects together provide 80% of the contribution to the prediction in step 7), then step 10 is followed. Otherwise, step 9, i. a return to step 5.

Method step 9: Since too many explanatory components were required, the core width is now reduced and proceeding with method step 5 and the new reduced core width.

Step 10: Since more than 50% of the chemical compounds require only less than five explanatory components, the current core width is retained and with exactly this core width (without further internal optimization) a Gaussian process model on the entire data set from method step 2 trained.

Process _Step 11: The models from process step 10 (GP _flt ) and process step 3 (GP _gen ) are both, together with the data set from process step 3 in a file stored and form the record-specific part of the program ToxExplain. By adding program code (which is not record specific) that provides this information at appropriate interfaces for visualization and model reduction, the program ToxExplain is created. The average errors and explanatory capabilities determined in method steps 5 to 9 are stored in a log file.

Process step 12: proper end.

The ToxTrain program (Figure 5) generates a program called ToxExplain from a record. This allows the automatically determined models to be used for new data.

Explanatory models of the type ToxExplain can be generated in the manner described in connection with FIG. 5 for any data records. These are each a program that (unlike previously available models) not only produces a prediction of the toxicity of chemical compounds, but also provides the following information at an interface:

• A list of exactly the connections in the training set on which the above prediction mainly relies (explanatory components). As described above, in step 6, the contributions to the sum are sorted by size according to equation (4), and then the connections are selected at the head of the list. The influence of these training compounds is quantified in percent.

• A list of the features of the new molecule that have the greatest impact on the prediction. The local Gradients of the core function for all features are calculated, normalized and sorted for the respective new molecule. The characteristics at the top of the list serve as optimization aids. Their influence is quantified in percent.

For the applying chemist, the information generated is useful when presented to him without context switching within his normal working environment. For visualization, existing programs for editing and visualizing molecules in the respective company are connected via interfaces and, if necessary, extended by plug-ins. At least the explanatory components (and their measured toxicity), the optimization aids, their respective proportions in percent, the structural formula of the new molecule and the prediction for the new molecule should be displayed simultaneously. An example of such a graph is found in FIG. 6.

In the upper part of FIG. 6, a prediction is shown, wherein the prediction for the new molecule is based primarily on two compounds from the training set. If the observing chemist considers these explanatory components to be plausible, the prediction makes his decision easier. The molecule A from the training set has an influence of 51% on the prediction, the molecule B has an influence of only 43%. This automatically confused finding is also automatically applied to the new molecule C, which is considered non-toxic.

In the lower part of Fig. 6, another example is shown. The molecule D should be changed so that it is no longer toxic. To the right of it are shown the structural features E, F of the molecule, which in the concrete case lead to the prediction being "toxic". These optimization aids make it easier for the chemist to specifically vary the new molecule so that it is no longer toxic i st.

In the following, another embodiment will be described, which is kept very simple for illustrative purposes. A training dataset with active and inactive molecules as well as two test molecules is used. The main aim is to show, by means of an example, how the explanatory components for kernel-based models are calculated and used.

Fig. 7 shows a training data set with active and inactive molecules and two test molecules with unknown activity. For the purposes of the example, the activity may be any property, such as binding to a receptor. Above a certain bond strength, molecules are called active, below they are called inactive. The molecules are represented by two numerical descriptors each, which are plotted on the X and Y axes. It should be noted that in real applications usually several hundred descriptors are used. The approach described here works the same way and is demonstrated here for the sake of clarity with two descriptors.

The coordinates and sequence numbers of the training molecules can be found in Tables 1 and 2 in columns A, B and C.

Table 1 in columns D and E contains the coordinates of test molecule 1 (identical for simplicity in all rows). Table 2 contains the analog information, but for test molecule 2.

In the following, the calculation of columns F to I will be explained.

For this example, we'll choose the RBF core function above already introduced as equation (2). Use in

Equation (1) leads to the following expression for the prediction f (x _new ):

The classes "Active" and "Inactive" are represented by the labels J = IW-IJ. Forecasts greater than or less than zero correspond to a classification as "Active" or "Inactive".

Although the prediction is not the actual topic of this discussion, it should be noted that both test molecules are given values above zero, thus classified as "active".

In Tables 1 and 2, the columns F contain the value of the selected RBF core function between the training molecule listed in the respective row and test molecule 1 (Table 1) and test molecule 2 (Table 2).

For the core width w determined in the training process, the value 2 is assumed in this example calculation.

As already mentioned above, in this example we assume that a fully trained kernel-based model with a weight vector OC already exists.

The columns G of Tables 1 and 2 contain, for each training molecule, the label-corrected entry of this weighting vector OC. It should be noted that there are two different definitions of OC, one of which

assumes fundamentally positive components of the vector OC, while the other carries the label J = IW-Ij _a ] _ _s sign of the respective component of 0t. The The definition used here assumes fundamentally positive O *.

In the present classification example, the correct definition can be ensured by a simple amount formation. In the regression case, the weight vector for kernel-based models has to be defined so that it has only positive entries, and the continuous labels are saved separately.

In general, the contribution of each training molecule is calculated as follows:

ß = k (x _new , _Xι ) -a (5)

In Tables 1 and 2, this value is found in columns H.

The standardized contribution of each training molecule:

denotes the proportion / percentage that each training molecule has _new in the prediction for the specific test molecule x. In Tables 1 and 2, this value is found in column I. where n stands for all training items that have become part of the model. Depending on the learning algorithm, this can be the entire training set (eg in the Gaussian process) or a subset of the training set. For support vector machines, this subset is called the support vectors.

For different test molecules whose representation (in form of descriptors), different values result for the components β.

In the present example we observe that the prediction of test molecule 1 is about 86% based on the number 5 training molecule, while all other training molecules contribute little to the prediction.

In contrast, the prediction for test molecule 2 is approximately 87% based on the training molecule number 5, while all other training molecules (again) contribute little to the prediction.

Sorting for β gives us a list of the training molecules in order of relevance for the prediction of the respective test molecule.

Thus, β represents a measure with which a ranking data record is automatically created, in which the measures of the influencing factors are arranged according to a predetermined condition. The method is thus to be understood as a kind of automatic measuring method for influencing factors, whereby this determination of the influencing factors enables further applications.

This is otherwise possible only if certain structures of the model are known. With the described embodiment, however, a reduced model is generated, which is then further usable, e.g. for control and regulation of a plant.

The person skilled in the art recognizes that this procedure can be used analogously for other properties.

Another application example results from the control engineering, eg the control of distillation columns. When high purities are required, In many cases, a distillation column behaves very non-linearly. Now, if the behavior of distillation columns is analyzed starting from a large training set of measured data (analogous to the procedure ToxTrain in Fig. 5), then a model is obtained which has explanatory components and optimization aids. This makes it possible to automatically simplify a very complex nonlinear model for specific purposes. Using the model reduction technique previously described using optimization tools, the number of features (perhaps large in a real plant) (eg, controlled variables and manipulated variables) can be automatically reduced, resulting in a simplified model. This is particularly useful when there is a large amount of training data from the past, which can be automatically reduced in this way, for example, to build a model-based control system.

In principle, other technical systems can also be examined by means of the described method in order to automatically determine specific influencing variables. For example, a model of a building could be used to determine the parameters that require particularly energy-efficient air conditioning. From a model of a production plant could e.g. automatically determine the parts of a production chain that represent a particular bottleneck or on which the quality of certain product elements is particularly sensitive. Similarly, other models of technical systems, e.g. electronic circuits or machines, automatically determining factors which may take the form of a reduced model e.g. are to be used for regulatory purposes.

Claims

claims A method of automatically analyzing a non-linear model for predicting properties of an a priori uncharacterized item, wherein a) the non-linear model based on a machine learning method, in particular a kernel-based learning method Training objects is formed so that it allows for at least one item a statement about at least one property, b) with an analysis means using the representative theorem, at least one measure number is automatically determined which indicates which training subject or which Training objects that have become part of the non-linear model have the greatest impact on the predictions of the non-linear model and c) automatically creates a ranking data set in which the measures of the influencing factors are arranged according to a predetermined condition. 2. The method according to claim 1, characterized in that by means of the rank data set automatically a model, in particular a non-linear model is formed whose complexity is lower due to the reduction due to the measures of the influencing factors, as the non-linear model, the was won from training. 3. The method according to claim 1 or 2, characterized in that as core-based Learning method uses a Gaussian process and / or a Support Vector Machine, Kernel Linear Discriminant Analysis (LDA), Kernel Partial Least Squares, Kernel Canonical Correlation Analysis, Kernel Ridge Regression. 4. The method according to at least one of the preceding claims, characterized in that the core width of a kernel-based learning method is optimized. 5. The method according to claim 4, characterized in that the kernel width is selectively reduced after the optimization, wherein as a criterion for the reduction, a threshold for an explanatory ability of the model is used. 6. The method according to at least one of the preceding claims, characterized in that from the non-linear model means ¥ ( ^χ _new ) 2w-Σa ₁ -y ₁ - (x _neuj -x _1J ) -e -Keu- ^χ ,) ² - ^w dxneu, j automatically optimization parameters can be determined. 7. The method according to at least one of the preceding claims, characterized in that in the processing of the training objects, a cross-validation or resampling strategy is used. 8. The method according to at least one of the preceding claims, characterized in that after the analysis which training subject or which training items, the part of the non-linear Have become models, the largest impact on the predictions of the non-linear model have automatically created a data set, in particular a program, with which a prediction of properties of the object is possible. 9. The method according to at least one of the preceding claims, characterized in that the objects are molecules that are features descriptive statements of the molecules that can be measured or calculated from their structural formula or estimate, especially belonging to the prior art chemical descriptors, in particular size , Weight, surface area and / or the number of functional groups, the structural formula itself, as well as properties that can be calculated using a structural matrix connectivity matrix, such as Eigenvalues of the connectivity matrix, the length of different paths through the graph, graph indices. 10. The method according to claim 9, characterized in that the structural formula of at least one molecule is formulated as a graph, so that this graph of graphene nuclei is processable. 11. The method according to at least one preceding claim 9, characterized in that the property to be predicted by means of the model is the toxicity, solubility in water and other solvents as water, melting point, boiling point, lipophilicity, acid or base constant, metabolic stability, or Binding to a receptor can be. 12. The method according to at least one of the preceding claims, characterized in that the objects plants, in particular chemical plants are from which temporary readings as Training objects are used and used as measured characteristics parameters of the plant. 13. The method according to claim 12, characterized in that the property of the plant, which should be predictable by means of the model, the product quality, a pressure, a temperature, a pH and / or a quantity is. 14. Device, in particular a Computer program product for automatically analyzing a non-linear model for predicting properties of an a priori uncharacterized object, a) with a machine learning means for forming the non-linear model from training objects, in particular with a core-based learning method, so that a statement about at least one property is possible for at least one object, b) with an analysis means using the Representer theorem automatically at least one measure is determinable, indicating which training subject or which Training objects that have become part of the non-linear model have the greatest impact on the predictions of the non-linear model and c) a rank data set can be created automatically, in which the measures of the influencing factors are arranged according to a predetermined condition.