Mario Marchand

Qi Chen, Mario Marchand

We use information-theoretic tools to derive a novel analysis of Multi-source Domain Adaptation (MDA) from the representation learning perspective. Concretely, we study joint distribution alignment for supervised MDA with few target labels and unsupervised MDA with pseudo labels, where the latter is relatively hard and less commonly studied. We further provide algorithm-dependent generalization bounds for these two settings, where the generalization is characterized by the mutual information between the parameters and the data. Then we propose a novel deep MDA algorithm, implicitly addressing the target shift through joint alignment. Finally, the mutual information bounds are extended to this algorithm providing a non-vacuous gradient-norm estimation. The proposed algorithm has comparable performance to the state-of-the-art on target-shifted MDA benchmark with improved memory efficiency.

Jean-Samuel Leboeuf, Frédéric LeBlanc, Mario Marchand

We revisit binary decision trees from the perspective of partitions of the data. We introduce the notion of partitioning function, and we relate it to the growth function and to the VC dimension. We consider three types of features: real-valued, categorical ordinal and categorical nominal, with different split rules for each. For each feature type, we upper bound the partitioning function of the class of decision stumps before extending the bounds to the class of general decision tree (of any fixed structure) using a recursive approach. Using these new results, we are able to find the exact VC dimension of decision stumps on examples of $\ell$ real-valued features, which is given by the largest integer $d$ such that $2\ell \ge \binom{d}{\lfloor\frac{d}{2}\rfloor}$. Furthermore, we show that the VC dimension of a binary tree structure with $L_T$ leaves on examples of $\ell$ real-valued features is in $O(L_T \log(L_T\ell))$. Finally, we elaborate a pruning algorithm based on these results that performs better than the cost-complexity and reduced-error pruning algorithms on a number of data sets, with the advantage that no cross-validation is required.

Abdelali Bouyahia, Frédéric LeBlanc, Mario Marchand

Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role remains only partially understood. In this work, we propose an information-theoretic framework that systematically accounts for the effect of augmentation on generalization and invariance learning. Our approach builds upon mutual information-based bounds, which relate the generalization gap to the amount of information a learning algorithm retains about its training data. We extend this framework by modeling the augmented distribution as a composition of the original data distribution with a distribution over transformations, which naturally induces an orbit-averaged loss function. Under mild sub-Gaussian assumptions on the loss function and the augmentation process, we derive a new generalization bound that decompose the expected generalization gap into three interpretable terms: (1) a distributional divergence between the original and augmented data, (2) a stability term measuring the algorithm dependence on training data, and (3) a sensitivity term capturing the effect of augmentation variability. To connect our bounds to the geometry of the augmentation group, we introduce the notion of group diameter, defined as the maximal perturbation that augmentations can induce in the input space. The group diameter provides a unified control parameter that bounds all three terms and highlights an intrinsic trade-off: small diameters preserve data fidelity but offer limited regularization, while large diameters enhance stability at the cost of increased bias and sensitivity. We validate our theoretical bounds with numerical experiments, demonstrating that it reliably tracks and predicts the behavior of the true generalization gap.

Wissam Akretche, Frédéric LeBlanc, Mario Marchand

In this work, we provide upper bounds on the risk of mixtures of experts by imposing local differential privacy (LDP) on their gating mechanism. These theoretical guarantees are tailored to mixtures of experts that utilize the one-out-of-$n$ gating mechanism, as opposed to the conventional $n$-out-of-$n$ mechanism. The bounds exhibit logarithmic dependence on the number of experts, and encapsulate the dependence on the gating mechanism in the LDP parameter, making them significantly tighter than existing bounds, under reasonable conditions. Experimental results support our theory, demonstrating that our approach enhances the generalization ability of mixtures of experts and validating the feasibility of imposing LDP on the gating mechanism.

Niffa Cheick Oumar Diaby, Thierry Duchesne, Mario Marchand

The predominance of machine learning models in many spheres of human activity has led to a growing demand for their transparency. The transparency of models makes it possible to discern some factors, such as security or non-discrimination. In this paper, we propose a mixture of transparent local models as an alternative solution for designing interpretable (or transparent) models. Our approach is designed for the situations where a simple and transparent function is suitable for modeling the label of instances in some localities/regions of the input space, but may change abruptly as we move from one locality to another. Consequently, the proposed algorithm is to learn both the transparent labeling function and the locality of the input space where the labeling function achieves a small risk in its assigned locality. By using a new multi-predictor (and multi-locality) loss function, we established rigorous PAC-Bayesian risk bounds for the case of binary linear classification problem and that of linear regression. In both cases, synthetic data sets were used to illustrate how the learning algorithms work. The results obtained from real data sets highlight the competitiveness of our approach compared to other existing methods as well as certain opaque models. Keywords: PAC-Bayes, risk bounds, local models, transparent models, mixtures of local transparent models.

Jean-Samuel Leboeuf, Frédéric LeBlanc, Mario Marchand

We significantly improve the generalization bounds for VC classes by using two main ideas. First, we consider the hypergeometric tail inversion to obtain a very tight non-uniform distribution-independent risk upper bound for VC classes. Second, we optimize the ghost sample trick to obtain a further non-negligible gain. These improvements are then used to derive a relative deviation bound, a multiclass margin bound, as well as a lower bound. Numerical comparisons show that the new bound is nearly never vacuous, and is tighter than other VC bounds for all reasonable data set sizes.

Gabriel Laberge, Yann Pequignot, Alexandre Mathieu et al.

Post-hoc global/local feature attribution methods are progressively being employed to understand the decisions of complex machine learning models. Yet, because of limited amounts of data, it is possible to obtain a diversity of models with good empirical performance but that provide very different explanations for the same prediction, making it hard to derive insight from them. In this work, instead of aiming at reducing the under-specification of model explanations, we fully embrace it and extract logical statements about feature attributions that are consistent across all models with good empirical performance (i.e. all models in the Rashomon Set). We show that partial orders of local/global feature importance arise from this methodology enabling more nuanced interpretations by allowing pairs of features to be incomparable when there is no consensus on their relative importance. We prove that every relation among features present in these partial orders also holds in the rankings provided by existing approaches. Finally, we present three use cases employing hypothesis spaces with tractable Rashomon Sets (Additive models, Kernel Ridge, and Random Forests) and show that partial orders allow one to extract consistent local and global interpretations of models despite their under-specification.

Qi Chen, Changjian Shui, Mario Marchand

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern model-agnostic meta-learning (MAML) algorithms. Moreover, we provide a data-dependent generalization bound for a stochastic variant of MAML, which is non-vacuous for deep few-shot learning. As compared to previous bounds that depend on the square norm of gradients, empirical validations on both simulated data and a well-known few-shot benchmark show that our bound is orders of magnitude tighter in most situations.

Jean-Samuel Leboeuf, Frédéric LeBlanc, Mario Marchand

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still weakly bounded. Hence, we revisit binary decision trees on real-valued features from the perspective of partitions of the data. We introduce the notion of partitioning function, and we relate it to the growth function and to the VC dimension. Using this new concept, we are able to find the exact VC dimension of decision stumps, which is given by the largest integer $d$ such that $2\ell \ge \binom{d}{\left\lfloor\frac{d}{2}\right\rfloor}$, where $\ell$ is the number of real-valued features. We provide a recursive expression to bound the partitioning functions, resulting in a upper bound on the growth function of any decision tree structure. This allows us to show that the VC dimension of a binary tree structure with $N$ internal nodes is of order $N \log(N\ell)$. Finally, we elaborate a pruning algorithm based on these results that performs better than the CART algorithm on a number of datasets, with the advantage that no cross-validation is required.

Prudencio Tossou, Basile Dura, Francois Laviolette et al.

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel operator that can be combined with a differentiable kernel algorithm during inference. While previous work within this framework has focused on learning a single kernel for large datasets, we learn a kernel family for a variety of few-shot regression tasks. Compared to single deep kernel learning, our algorithm enables the identification of the appropriate kernel for each task during inference. As such, it is well adapted for complex task distributions in a few-shot learning setting, which we demonstrate by comparing against existing state-of-the-art algorithms using real-world, few-shot regression tasks related to the field of drug discovery.

Alexandre Drouin, Frédéric Raymond, Gaël Letarte St-Pierre et al.

Antimicrobial resistance is an important public health concern that has implications in the practice of medicine worldwide. Accurately predicting resistance phenotypes from genome sequences shows great promise in promoting better use of antimicrobial agents, by determining which antibiotics are likely to be effective in specific clinical cases. In healthcare, this would allow for the design of treatment plans tailored for specific individuals, likely resulting in better clinical outcomes for patients with bacterial infections. In this work, we present the recent work of Drouin et al. (2016) on using Set Covering Machines to learn highly interpretable models of antibiotic resistance and complement it by providing a large scale application of their method to the entire PATRIC database. We report prediction results for 36 new datasets and present the Kover AMR platform, a new web-based tool allowing the visualization and interpretation of the generated models.

Louis Fortier-Dubois, François Laviolette, Mario Marchand et al.

We first present a general risk bound for ensembles that depends on the Lp norm of the weighted combination of voters which can be selected from a continuous set. We then propose a boosting method, called QuadBoost, which is strongly supported by the general risk bound and has very simple rules for assigning the voters' weights. Moreover, QuadBoost exhibits a rate of decrease of its empirical error which is slightly faster than the one achieved by AdaBoost. The experimental results confirm the expectation of the theory that QuadBoost is a very efficient method for learning ensembles.

Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan et al.

We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired by the theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on features that cannot discriminate between the training (source) and test (target) domains. The approach implements this idea in the context of neural network architectures that are trained on labeled data from the source domain and unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of features that are (i) discriminative for the main learning task on the source domain and (ii) indiscriminate with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation and stochastic gradient descent, and can thus be implemented with little effort using any of the deep learning packages. We demonstrate the success of our approach for two distinct classification problems (document sentiment analysis and image classification), where state-of-the-art domain adaptation performance on standard benchmarks is achieved. We also validate the approach for descriptor learning task in the context of person re-identification application.

Alexandre Drouin, Sébastien Giguère, Maxime Déraspe et al.

The Set Covering Machine (SCM) is a greedy learning algorithm that produces sparse classifiers. We extend the SCM for datasets that contain a huge number of features. The whole genetic material of living organisms is an example of such a case, where the number of feature exceeds 10^7. Three human pathogens were used to evaluate the performance of the SCM at predicting antimicrobial resistance. Our results show that the SCM compares favorably in terms of sparsity and accuracy against L1 and L2 regularized Support Vector Machines and CART decision trees. Moreover, the SCM was the only algorithm that could consider the full feature space. For all other algorithms, the latter had to be filtered as a preprocessing step.

Pascal Germain, Alexandre Lacasse, François Laviolette et al.

We propose an extensive analysis of the behavior of majority votes in binary classification. In particular, we introduce a risk bound for majority votes, called the C-bound, that takes into account the average quality of the voters and their average disagreement. We also propose an extensive PAC-Bayesian analysis that shows how the C-bound can be estimated from various observations contained in the training data. The analysis intends to be self-contained and can be used as introductory material to PAC-Bayesian statistical learning theory. It starts from a general PAC-Bayesian perspective and ends with uncommon PAC-Bayesian bounds. Some of these bounds contain no Kullback-Leibler divergence and others allow kernel functions to be used as voters (via the sample compression setting). Finally, out of the analysis, we propose the MinCq learning algorithm that basically minimizes the C-bound. MinCq reduces to a simple quadratic program. Aside from being theoretically grounded, MinCq achieves state-of-the-art performance, as shown in our extensive empirical comparison with both AdaBoost and the Support Vector Machine.

Hana Ajakan, Pascal Germain, Hugo Larochelle et al.

We introduce a new representation learning algorithm suited to the context of domain adaptation, in which data at training and test time come from similar but different distributions. Our algorithm is directly inspired by theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on a data representation that cannot discriminate between the training (source) and test (target) domains. We propose a training objective that implements this idea in the context of a neural network, whose hidden layer is trained to be predictive of the classification task, but uninformative as to the domain of the input. Our experiments on a sentiment analysis classification benchmark, where the target domain data available at training time is unlabeled, show that our neural network for domain adaption algorithm has better performance than either a standard neural network or an SVM, even if trained on input features extracted with the state-of-the-art marginalized stacked denoising autoencoders of Chen et al. (2012).

Sébastien Giguère, Amélie Rolland, François Laviolette et al.

The pre-image problem has to be solved during inference by most structured output predictors. For string kernels, this problem corresponds to finding the string associated to a given input. An algorithm capable of solving or finding good approximations to this problem would have many applications in computational biology and other fields. This work uses a recent result on combinatorial optimization of linear predictors based on string kernels to develop, for the pre-image, a low complexity upper bound valid for many string kernels. This upper bound is used with success in a branch and bound searching algorithm. Applications and results in the discovery of druggable peptides are presented and discussed.

Alexandre Drouin, Sébastien Giguère, Vladana Sagatovich et al.

The increased affordability of whole genome sequencing has motivated its use for phenotypic studies. We address the problem of learning interpretable models for discrete phenotypes from whole genomes. We propose a general approach that relies on the Set Covering Machine and a k-mer representation of the genomes. We show results for the problem of predicting the resistance of Pseudomonas Aeruginosa, an important human pathogen, against 4 antibiotics. Our results demonstrate that extremely sparse models which are biologically relevant can be learnt using this approach.

Alexandre Lacoste, Hugo Larochelle, François Laviolette et al.

One of the most tedious tasks in the application of machine learning is model selection, i.e. hyperparameter selection. Fortunately, recent progress has been made in the automation of this process, through the use of sequential model-based optimization (SMBO) methods. This can be used to optimize a cross-validation performance of a learning algorithm over the value of its hyperparameters. However, it is well known that ensembles of learned models almost consistently outperform a single model, even if properly selected. In this paper, we thus propose an extension of SMBO methods that automatically constructs such ensembles. This method builds on a recently proposed ensemble construction paradigm known as agnostic Bayesian learning. In experiments on 22 regression and 39 classification data sets, we confirm the success of this proposed approach, which is able to outperform model selection with SMBO.

Sébastien Giguère, Mario Marchand, François Laviolette et al.

We propose a specialized string kernel for small bio-molecules, peptides and pseudo-sequences of binding interfaces. The kernel incorporates physico-chemical properties of amino acids and elegantly generalize eight kernels, such as the Oligo, the Weighted Degree, the Blended Spectrum, and the Radial Basis Function. We provide a low complexity dynamic programming algorithm for the exact computation of the kernel and a linear time algorithm for it's approximation. Combined with kernel ridge regression and SupCK, a novel binding pocket kernel, the proposed kernel yields biologically relevant and good prediction accuracy on the PepX database. For the first time, a machine learning predictor is capable of accurately predicting the binding affinity of any peptide to any protein. The method was also applied to both single-target and pan-specific Major Histocompatibility Complex class II benchmark datasets and three Quantitative Structure Affinity Model benchmark datasets. On all benchmarks, our method significantly (p-value < 0.057) outperforms the current state-of-the-art methods at predicting peptide-protein binding affinities. The proposed approach is flexible and can be applied to predict any quantitative biological activity. The method should be of value to a large segment of the research community with the potential to accelerate peptide-based drug and vaccine development.