Structural libraries of fragments are commonly used to model or design the 3D structure of biomol... more Structural libraries of fragments are commonly used to model or design the 3D structure of biomolecules (drugs, peptides, nucleic acids). They typically approximate all possible local conformations of these molecules within a given precision, by a set of wellchosen representative fragments. Such a set can be obtained by clustering a larger set of fragments whose structures have been solved experimentally, using suitable clustering algorithm and measure of dissimilarity between fragments. A commonly used measure of dissimilarity in structural biology is the root mean square deviation (RMSD), whose exact computation requires a pairwise structural alignment. But this alignment is highly time-consuming and not applicable for a very large initial set of fragments. We propose here an approach based on feature extraction to perform an effective clustering, while avoiding a computationally expensive full pairwise alignment. Using as example poly-A RNA fragments of 3 nucleotides (3-nt), we s...
<b>Copyright information:</b>Taken from "Prediction of amphipathic in-plane memb... more <b>Copyright information:</b>Taken from "Prediction of amphipathic in-plane membrane anchors in monotopic proteins using a SVM classifier"BMC Bioinformatics 2006;7():255-255.Published online 16 May 2006PMCID:PMC1564421.sition of IPM anchors is shown in black, of TM helices in grey and of solvent-accessible helices from globular proteins in white. IPM anchors are extracted from our final data set. Solvent accessible helices are extracted from globular soluble proteins present in the PDB (sequence similarity lower than 25%, accessibility computed by DSSP [53] lower than or equal to 60). TM helices are extracted from the 3D_helix set of the MPtopo database [5].
Motivation Atomistic models of nucleic acids (NA) fragments can be used to model the 3D structure... more Motivation Atomistic models of nucleic acids (NA) fragments can be used to model the 3D structures of specific protein–NA interactions and address the problem of great NA flexibility, especially in their single-stranded regions. One way to obtain relevant NA fragments is to extract them from existing 3D structures corresponding to the targeted context (e.g. specific 2D structures, protein families, sequences) and to learn from them. Several databases exist for specific NA 3D motifs, especially in RNA, but none can handle the variety of possible contexts. Results This article presents protNAff (protein-bound Nucleic Acids filters and fragments), a new pipeline for the conception of searchable databases on the 2D and 3D structures of protein-bound NA, the selection of context-specific (regions of) NA structures by combinations of filters, and the creation of context-specific NA fragment libraries. The strength of this pipeline is its modularity, allowing users to adapt it to many spec...
We study inductive matrix completion (matrix completion with side information) under an i.i.d. su... more We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the standard deviation of the noise and in particular approach zero in the exact recovery case; (2) even in the presence of noise, they converge to zero when the sample size approaches infinity; and (3) for a fixed dimension of the side information, they only have a logarithmic dependence on the size of the matrix. Differently from many works in approximate recovery, we present results both for bounded Lipschitz losses and for the absolute loss, with the latter relying on Talagrand-type inequalities. The proofs create a bridge between two approaches to the theoretical analysis of matrix completion, since they consist in a combination of techniques from both the exact recovery literature and the approximate recovery literature.
International audienceOne of the main open problems of the theory of margin multi-category patter... more International audienceOne of the main open problems of the theory of margin multi-category pattern classification is the characterization of the optimal dependence of the confidence interval of a guaranteed risk on the three basic parameters which are the sample size m, the number C of categories and the scale parameter γ. This is especially the case when working under minimal learn-ability hypotheses. The starting point is a basic supremum inequality whose capacity measure depends on the choice of the margin loss function. Then, transitions are made, from capacity measure to capacity measure. At some level, a structural result performs the transition from the multi-class case to the bi-class one. In this article, we highlight the advantages and drawbacks inherent to the three major options for this decomposition: using Rademacher complexities, covering numbers or scale-sensitive combinatorial dimensions
Some of the most recent developments are presented in multidimensional spectrosocpic data extract... more Some of the most recent developments are presented in multidimensional spectrosocpic data extraction and classification of non- and pre-cancerous skin tissues using Spaatially Resolved Multiple Excitation AutoFluorescence and Diffuse Reflectance Spectroscopies
We introduce an extension of our fragment-based method for ssRNA-protein docking as it is still a... more We introduce an extension of our fragment-based method for ssRNA-protein docking as it is still a challenging difficulty in docking. It is dedicated to hairpins and makes use of geometrical features of this secondary structure. An initial evaluation establishes that it is promising and could make it possible to overcome the limitations of the state-of-the-art fragment-based methods.
2017 Asia Communications and Photonics Conference (ACP), 2017
After a general overview on the various types of features extracted and on the main selection and... more After a general overview on the various types of features extracted and on the main selection and classification methods implemented in the frame of tissue fibered spectroscopy studies, the present contribution will focus on the implementation of multi-class classification schemes and the original combination of decision fusion approaches based on AutoFluorescence (AF) and Diffuse Reflectance (DR) modalities and spatial resolution through multiple Collecting- Excitation Fiber Distances (CEFS). Results confirm the interest to couple AF and DR spectroscopy measurements and show that this innovative solution based on spatial resolution data fusion leads to optimized discrimination between histological classes and reduced confusion between the closest histological classes.
This article deals with the generalization performance of margin multi-category classi ers, when ... more This article deals with the generalization performance of margin multi-category classi ers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures belonging to three main families: Rademacher/Gaussian complexities, metric entropies and scale-sensitive combinatorial dimensions. The scale-sensitive combinatorial dimensions dedicated to the classi ers of this kind are the γ-Ψ-dimensions. We introduce the combinatorial and structural results needed to involve them in the derivation of guaranteed risks and establish the corresponding upper bounds on the metric entropies and the Rademacher complexity. Two major conclusions can be drawn: 1. the γ-Ψ-dimensions always bring an improvement compared to the use of the fat-shattering dimension of the class of margin functions; 2. thanks to their capacity to take into account basic features of the classi er, they represent a promising alternative to perform...
Bounds on the risk play a crucial role in statistical learning theory. They usually involve as ca... more Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such “VC dimensions” exist for models taking values in {0, 1}, {1, . . . , Q} and R. We introduce the generalizations appropriate for the missing case, the one of models with values in R. This provides us with a new guaranteed risk for M-SVMs which appears superior to the existing one.
Clinical and Biomedical Spectroscopy and Imaging IV, 2015
The current study deals with new perspectives to perform more efficient classification of mouse s... more The current study deals with new perspectives to perform more efficient classification of mouse skin precancerous stages by means of a decision fusion scheme based on belief functions and exploiting the spatial resolution of the autofluorescence and diffuse reflectance spectroscopic data.
One of the main open problems in the theory of margin multicategory pattern classification is the... more One of the main open problems in the theory of margin multicategory pattern classification is the dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter γ. This paper derives a new bound on the probability of error of margin multicategory classifiers under minimal learnability assumptions. It improves the dependency on C over the state of the art. This is achieved through the introduction of a new Sauer-Shelah lemma.
This article deals with the generalization performance of margin multi-category classifiers, when... more This article deals with the generalization performance of margin multi-category classifiers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures belonging to three main families: Rademacher/Gaussian complexities, metric entropies and scale-sensitive combinatorial dimensions. The scale-sensitive combinatorial dimensions dedicated to the classifiers of this kind are the gamma-Psi-dimensions. We introduce the combinatorial and structural results needed to involve them in the derivation of upper bounds on the metric entropies and the Rademacher complexity. Their incidence on the guaranteed risks is characterized, which establishes that in the theoretical framework of interest, performing the transition from the multi-class case to the binary one with combinatorial dimensions is a promising alternative to proceeding with covering numbers.
In the context of discriminant analysis, Vapnik's statistical learning theory has mainly been... more In the context of discriminant analysis, Vapnik's statistical learning theory has mainly been developed in three directions: the computation of dichotomies with binary-valued functions, the computation of dichotomies with real-valued functions, and the computation of polytomies with functions taking their values in finite sets, typically the set of categories itself. The case of classes of vector-valued functions used to compute polytomies has seldom been considered independently, which is unsatisfactory, for three main reasons. First, this case encompasses the other ones. Second, it cannot be treated appropriately through a naive extension of the results devoted to the computation of dichotomies. Third, most of the classification problems met in practice involve multiple categories. In this paper, a VC theory of large margin multi-category classifiers is introduced. Central in this theory are generalized VC dimensions called the γ-Ψ-dimensions. First, a uniform convergence boun...
To set the values of the hyperparameters of a support vector machine (SVM), the method of choice ... more To set the values of the hyperparameters of a support vector machine (SVM), the method of choice is cross-validation. Several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. One of the most popular is the radius-margin bound. It applies to the hard margin machine, and, by extension, to the 2-norm SVM. In this article, we introduce the first quadratic loss multi-class SVM: the M-SVM 2. It can be seen as a direct extension of the 2-norm SVM to the multi-class case, which we establish by deriving the corresponding generalized radius-margin bound.
One of the main open problems in the theory of multi-category margin classification is the form o... more One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter γ. From a practical point of view, the theoretical analysis of generalization performance contributes to the development of new learning algorithms. In this paper, we focus only on the theoretical aspect of the question posed. More precisely, under minimal learnability assumptions, we derive a new risk bound for multi-category margin classifiers. We improve the dependency on C over the state of the art when the margin loss function considered satisfies the Lipschitz condition. We start with the basic supremum inequality that involves a Rademacher complexity as a capacity measure. This capacity measure is then linked to the metric entropy through the chaining method. In this context, our improvement is based on the introduction of a new combinatorial metric entropy bound.
One of the main open problems of the theory of margin multicategory pattern classification is the... more One of the main open problems of the theory of margin multicategory pattern classification is the characterization of the optimal dependence of the confidence interval of a guaranteed risk on the three basic parameters which are the sample size m, the number C of categories and the scale parameter γ. This is especially the case when working under minimal learnability hypotheses. The starting point is a basic supremum inequality whose capacity measure depends on the choice of the margin loss function. Then, transitions are made, from capacity measure to capacity measure. At some level, a structural result performs the transition from the multi-class case to the bi-class one. In this article, we highlight the advantages and drawbacks inherent to the three major options for this decomposition: using Rademacher complexities, covering numbers or scale-sensitive combinatorial dimensions.
In the framework of agnostic learning, one of the main open problems of the theory of multi-categ... more In the framework of agnostic learning, one of the main open problems of the theory of multi-category pattern classification is the characterization of the way the complexity varies with the number C of categories. More precisely, if the classifier is characterized only through minimal learnability hypotheses, then the optimal dependency on C that an upper bound on the probability of error should exhibit is unknown. We consider margin classifiers. They are based on classes of vector-valued functions with one component function per category, and the classes of component functions are uniform Glivenko-Cantelli classes. For these classifiers, an L p-norm Sauer-Shelah lemma is established. It is then used to derive guaranteed risks in the L ∞ and L 2-norms. These bounds improve over the state-of-the-art ones with respect to their dependency on C, which is sublinear.
Structural libraries of fragments are commonly used to model or design the 3D structure of biomol... more Structural libraries of fragments are commonly used to model or design the 3D structure of biomolecules (drugs, peptides, nucleic acids). They typically approximate all possible local conformations of these molecules within a given precision, by a set of wellchosen representative fragments. Such a set can be obtained by clustering a larger set of fragments whose structures have been solved experimentally, using suitable clustering algorithm and measure of dissimilarity between fragments. A commonly used measure of dissimilarity in structural biology is the root mean square deviation (RMSD), whose exact computation requires a pairwise structural alignment. But this alignment is highly time-consuming and not applicable for a very large initial set of fragments. We propose here an approach based on feature extraction to perform an effective clustering, while avoiding a computationally expensive full pairwise alignment. Using as example poly-A RNA fragments of 3 nucleotides (3-nt), we s...
<b>Copyright information:</b>Taken from "Prediction of amphipathic in-plane memb... more <b>Copyright information:</b>Taken from "Prediction of amphipathic in-plane membrane anchors in monotopic proteins using a SVM classifier"BMC Bioinformatics 2006;7():255-255.Published online 16 May 2006PMCID:PMC1564421.sition of IPM anchors is shown in black, of TM helices in grey and of solvent-accessible helices from globular proteins in white. IPM anchors are extracted from our final data set. Solvent accessible helices are extracted from globular soluble proteins present in the PDB (sequence similarity lower than 25%, accessibility computed by DSSP [53] lower than or equal to 60). TM helices are extracted from the 3D_helix set of the MPtopo database [5].
Motivation Atomistic models of nucleic acids (NA) fragments can be used to model the 3D structure... more Motivation Atomistic models of nucleic acids (NA) fragments can be used to model the 3D structures of specific protein–NA interactions and address the problem of great NA flexibility, especially in their single-stranded regions. One way to obtain relevant NA fragments is to extract them from existing 3D structures corresponding to the targeted context (e.g. specific 2D structures, protein families, sequences) and to learn from them. Several databases exist for specific NA 3D motifs, especially in RNA, but none can handle the variety of possible contexts. Results This article presents protNAff (protein-bound Nucleic Acids filters and fragments), a new pipeline for the conception of searchable databases on the 2D and 3D structures of protein-bound NA, the selection of context-specific (regions of) NA structures by combinations of filters, and the creation of context-specific NA fragment libraries. The strength of this pipeline is its modularity, allowing users to adapt it to many spec...
We study inductive matrix completion (matrix completion with side information) under an i.i.d. su... more We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the standard deviation of the noise and in particular approach zero in the exact recovery case; (2) even in the presence of noise, they converge to zero when the sample size approaches infinity; and (3) for a fixed dimension of the side information, they only have a logarithmic dependence on the size of the matrix. Differently from many works in approximate recovery, we present results both for bounded Lipschitz losses and for the absolute loss, with the latter relying on Talagrand-type inequalities. The proofs create a bridge between two approaches to the theoretical analysis of matrix completion, since they consist in a combination of techniques from both the exact recovery literature and the approximate recovery literature.
International audienceOne of the main open problems of the theory of margin multi-category patter... more International audienceOne of the main open problems of the theory of margin multi-category pattern classification is the characterization of the optimal dependence of the confidence interval of a guaranteed risk on the three basic parameters which are the sample size m, the number C of categories and the scale parameter γ. This is especially the case when working under minimal learn-ability hypotheses. The starting point is a basic supremum inequality whose capacity measure depends on the choice of the margin loss function. Then, transitions are made, from capacity measure to capacity measure. At some level, a structural result performs the transition from the multi-class case to the bi-class one. In this article, we highlight the advantages and drawbacks inherent to the three major options for this decomposition: using Rademacher complexities, covering numbers or scale-sensitive combinatorial dimensions
Some of the most recent developments are presented in multidimensional spectrosocpic data extract... more Some of the most recent developments are presented in multidimensional spectrosocpic data extraction and classification of non- and pre-cancerous skin tissues using Spaatially Resolved Multiple Excitation AutoFluorescence and Diffuse Reflectance Spectroscopies
We introduce an extension of our fragment-based method for ssRNA-protein docking as it is still a... more We introduce an extension of our fragment-based method for ssRNA-protein docking as it is still a challenging difficulty in docking. It is dedicated to hairpins and makes use of geometrical features of this secondary structure. An initial evaluation establishes that it is promising and could make it possible to overcome the limitations of the state-of-the-art fragment-based methods.
2017 Asia Communications and Photonics Conference (ACP), 2017
After a general overview on the various types of features extracted and on the main selection and... more After a general overview on the various types of features extracted and on the main selection and classification methods implemented in the frame of tissue fibered spectroscopy studies, the present contribution will focus on the implementation of multi-class classification schemes and the original combination of decision fusion approaches based on AutoFluorescence (AF) and Diffuse Reflectance (DR) modalities and spatial resolution through multiple Collecting- Excitation Fiber Distances (CEFS). Results confirm the interest to couple AF and DR spectroscopy measurements and show that this innovative solution based on spatial resolution data fusion leads to optimized discrimination between histological classes and reduced confusion between the closest histological classes.
This article deals with the generalization performance of margin multi-category classi ers, when ... more This article deals with the generalization performance of margin multi-category classi ers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures belonging to three main families: Rademacher/Gaussian complexities, metric entropies and scale-sensitive combinatorial dimensions. The scale-sensitive combinatorial dimensions dedicated to the classi ers of this kind are the γ-Ψ-dimensions. We introduce the combinatorial and structural results needed to involve them in the derivation of guaranteed risks and establish the corresponding upper bounds on the metric entropies and the Rademacher complexity. Two major conclusions can be drawn: 1. the γ-Ψ-dimensions always bring an improvement compared to the use of the fat-shattering dimension of the class of margin functions; 2. thanks to their capacity to take into account basic features of the classi er, they represent a promising alternative to perform...
Bounds on the risk play a crucial role in statistical learning theory. They usually involve as ca... more Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such “VC dimensions” exist for models taking values in {0, 1}, {1, . . . , Q} and R. We introduce the generalizations appropriate for the missing case, the one of models with values in R. This provides us with a new guaranteed risk for M-SVMs which appears superior to the existing one.
Clinical and Biomedical Spectroscopy and Imaging IV, 2015
The current study deals with new perspectives to perform more efficient classification of mouse s... more The current study deals with new perspectives to perform more efficient classification of mouse skin precancerous stages by means of a decision fusion scheme based on belief functions and exploiting the spatial resolution of the autofluorescence and diffuse reflectance spectroscopic data.
One of the main open problems in the theory of margin multicategory pattern classification is the... more One of the main open problems in the theory of margin multicategory pattern classification is the dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter γ. This paper derives a new bound on the probability of error of margin multicategory classifiers under minimal learnability assumptions. It improves the dependency on C over the state of the art. This is achieved through the introduction of a new Sauer-Shelah lemma.
This article deals with the generalization performance of margin multi-category classifiers, when... more This article deals with the generalization performance of margin multi-category classifiers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures belonging to three main families: Rademacher/Gaussian complexities, metric entropies and scale-sensitive combinatorial dimensions. The scale-sensitive combinatorial dimensions dedicated to the classifiers of this kind are the gamma-Psi-dimensions. We introduce the combinatorial and structural results needed to involve them in the derivation of upper bounds on the metric entropies and the Rademacher complexity. Their incidence on the guaranteed risks is characterized, which establishes that in the theoretical framework of interest, performing the transition from the multi-class case to the binary one with combinatorial dimensions is a promising alternative to proceeding with covering numbers.
In the context of discriminant analysis, Vapnik's statistical learning theory has mainly been... more In the context of discriminant analysis, Vapnik's statistical learning theory has mainly been developed in three directions: the computation of dichotomies with binary-valued functions, the computation of dichotomies with real-valued functions, and the computation of polytomies with functions taking their values in finite sets, typically the set of categories itself. The case of classes of vector-valued functions used to compute polytomies has seldom been considered independently, which is unsatisfactory, for three main reasons. First, this case encompasses the other ones. Second, it cannot be treated appropriately through a naive extension of the results devoted to the computation of dichotomies. Third, most of the classification problems met in practice involve multiple categories. In this paper, a VC theory of large margin multi-category classifiers is introduced. Central in this theory are generalized VC dimensions called the γ-Ψ-dimensions. First, a uniform convergence boun...
To set the values of the hyperparameters of a support vector machine (SVM), the method of choice ... more To set the values of the hyperparameters of a support vector machine (SVM), the method of choice is cross-validation. Several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. One of the most popular is the radius-margin bound. It applies to the hard margin machine, and, by extension, to the 2-norm SVM. In this article, we introduce the first quadratic loss multi-class SVM: the M-SVM 2. It can be seen as a direct extension of the 2-norm SVM to the multi-class case, which we establish by deriving the corresponding generalized radius-margin bound.
One of the main open problems in the theory of multi-category margin classification is the form o... more One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter γ. From a practical point of view, the theoretical analysis of generalization performance contributes to the development of new learning algorithms. In this paper, we focus only on the theoretical aspect of the question posed. More precisely, under minimal learnability assumptions, we derive a new risk bound for multi-category margin classifiers. We improve the dependency on C over the state of the art when the margin loss function considered satisfies the Lipschitz condition. We start with the basic supremum inequality that involves a Rademacher complexity as a capacity measure. This capacity measure is then linked to the metric entropy through the chaining method. In this context, our improvement is based on the introduction of a new combinatorial metric entropy bound.
One of the main open problems of the theory of margin multicategory pattern classification is the... more One of the main open problems of the theory of margin multicategory pattern classification is the characterization of the optimal dependence of the confidence interval of a guaranteed risk on the three basic parameters which are the sample size m, the number C of categories and the scale parameter γ. This is especially the case when working under minimal learnability hypotheses. The starting point is a basic supremum inequality whose capacity measure depends on the choice of the margin loss function. Then, transitions are made, from capacity measure to capacity measure. At some level, a structural result performs the transition from the multi-class case to the bi-class one. In this article, we highlight the advantages and drawbacks inherent to the three major options for this decomposition: using Rademacher complexities, covering numbers or scale-sensitive combinatorial dimensions.
In the framework of agnostic learning, one of the main open problems of the theory of multi-categ... more In the framework of agnostic learning, one of the main open problems of the theory of multi-category pattern classification is the characterization of the way the complexity varies with the number C of categories. More precisely, if the classifier is characterized only through minimal learnability hypotheses, then the optimal dependency on C that an upper bound on the probability of error should exhibit is unknown. We consider margin classifiers. They are based on classes of vector-valued functions with one component function per category, and the classes of component functions are uniform Glivenko-Cantelli classes. For these classifiers, an L p-norm Sauer-Shelah lemma is established. It is then used to derive guaranteed risks in the L ∞ and L 2-norms. These bounds improve over the state-of-the-art ones with respect to their dependency on C, which is sublinear.
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Papers by Yann Guermeur