97 research outputs found
Rounding Methods for Discrete Linear Classification (Extended Version)
Learning discrete linear classifiers is known as a difficult challenge. In this paper, this learning task is cast as combinatorial optimization problem: given a training sample formed by positive and negative feature vectors in the Euclidean space, the goal is to find a discrete linear function that minimizes the cumulative hinge loss of the sample. Since this problem is NP-hard, we examine two simple rounding algorithms that discretize the fractional solution of the problem. Generalization bounds are derived for several classes of binary-weighted linear functions, by analyzing the Rademacher complexity of these classes and by establishing approximation bounds for our rounding algorithms. Our methods are evaluated on both synthetic and real-world data
Deep Learning for Metagenomic Data: using 2D Embeddings and Convolutional Neural Networks
Deep learning (DL) techniques have had unprecedented success when applied to
images, waveforms, and texts to cite a few. In general, when the sample size
(N) is much greater than the number of features (d), DL outperforms previous
machine learning (ML) techniques, often through the use of convolution neural
networks (CNNs). However, in many bioinformatics ML tasks, we encounter the
opposite situation where d is greater than N. In these situations, applying DL
techniques (such as feed-forward networks) would lead to severe overfitting.
Thus, sparse ML techniques (such as LASSO e.g.) usually yield the best results
on these tasks. In this paper, we show how to apply CNNs on data which do not
have originally an image structure (in particular on metagenomic data). Our
first contribution is to show how to map metagenomic data in a meaningful way
to 1D or 2D images. Based on this representation, we then apply a CNN, with the
aim of predicting various diseases. The proposed approach is applied on six
different datasets including in total over 1000 samples from various diseases.
This approach could be a promising one for prediction tasks in the
bioinformatics field.Comment: Accepted at NIPS 2017 Workshop on Machine Learning for Health
(https://ml4health.github.io/2017/); In Proceedings of the NIPS ML4H 2017
Workshop in Long Beach, CA, USA
The Power of Swap Deals in Distributed Resource Allocation
International audienceIn the simple resource allocation setting consisting in assigning exactly one resource per agent, the top trading cycle procedure stands out as being the undisputed method of choice. It remains however a centralized procedure which may not well suited in the context of multiagent systems, where distributed coordination may be problematic. In this paper, we investigate the power of dynamics based on rational bilateral deals (swaps) in such settings. While they may induce a high efficiency loss, we provide several new elements that temper this fact: (i) we identify a natural domain where convergence to a Pareto-optimal allocation can be guaranteed, (ii) we show that the worst-case loss of welfare is as good as it can be under the assumption of individual rationality, (iii) we provide a number of experimental results, showing that such dynamics often provide good outcomes, especially in light of their simplicity, and (iv) we prove the NP-hardness of deciding whether an allocation maximizing utilitarian or egalitarian welfare is reachable
On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory
This paper tackles the problem of Lipschitz regularization of Convolutional
Neural Networks. Lipschitz regularity is now established as a key property of
modern deep learning with implications in training stability, generalization,
robustness against adversarial examples, etc. However, computing the exact
value of the Lipschitz constant of a neural network is known to be NP-hard.
Recent attempts from the literature introduce upper bounds to approximate this
constant that are either efficient but loose or accurate but computationally
expensive. In this work, by leveraging the theory of Toeplitz matrices, we
introduce a new upper bound for convolutional layers that is both tight and
easy to compute. Based on this result we devise an algorithm to train Lipschitz
regularized Convolutional Neural Networks
Online Trajectory Planning Through Combined Trajectory Optimization and Function Approximation: Application to the Exoskeleton Atalante
Autonomous robots require online trajectory planning capability to operate in
the real world. Efficient offline trajectory planning methods already exist,
but are computationally demanding, preventing their use online. In this paper,
we present a novel algorithm called Guided Trajectory Learning that learns a
function approximation of solutions computed through trajectory optimization
while ensuring accurate and reliable predictions. This function approximation
is then used online to generate trajectories. This algorithm is designed to be
easy to implement, and practical since it does not require massive computing
power. It is readily applicable to any robotics systems and effortless to set
up on real hardware since robust control strategies are usually already
available. We demonstrate the computational performance of our algorithm on
flat-foot walking with the self-balanced exoskeleton Atalante
Randomization for adversarial robustness: the Good, the Bad and the Ugly
Deep neural networks are known to be vulnerable to adversarial attacks: A
small perturbation that is imperceptible to a human can easily make a
well-trained deep neural network misclassify. To defend against adversarial
attacks, randomized classifiers have been proposed as a robust alternative to
deterministic ones. In this work we show that in the binary classification
setting, for any randomized classifier, there is always a deterministic
classifier with better adversarial risk. In other words, randomization is not
necessary for robustness. In many common randomization schemes, the
deterministic classifiers with better risk are explicitly described: For
example, we show that ensembles of classifiers are more robust than mixtures of
classifiers, and randomized smoothing is more robust than input noise
injection. Finally, experiments confirm our theoretical results with the two
families of randomized classifiers we analyze.Comment: 8 pages + bibliography and appendix, 3 figures. Submitted to ICML
202
Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modelling
As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions
Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows
Achieving a balance between image quality (precision) and diversity (recall)
is a significant challenge in the domain of generative models. Current
state-of-the-art models primarily rely on optimizing heuristics, such as the
Fr\'echet Inception Distance. While recent developments have introduced
principled methods for evaluating precision and recall, they have yet to be
successfully integrated into the training of generative models. Our main
contribution is a novel training method for generative models, such as
Generative Adversarial Networks and Normalizing Flows, which explicitly
optimizes a user-defined trade-off between precision and recall. More
precisely, we show that achieving a specified precision-recall trade-off
corresponds to minimizing a unique -divergence from a family we call the
\mbox{\em PR-divergences}. Conversely, any -divergence can be written as a
linear combination of PR-divergences and corresponds to a weighted
precision-recall trade-off. Through comprehensive evaluations, we show that our
approach improves the performance of existing state-of-the-art models like
BigGAN in terms of either precision or recall when tested on datasets such as
ImageNet
Reactive Stepping for Humanoid Robots using Reinforcement Learning: Application to Standing Push Recovery on the Exoskeleton Atalante
State-of-the-art reinforcement learning is now able to learn versatile
locomotion, balancing and push-recovery capabilities for bipedal robots in
simulation. Yet, the reality gap has mostly been overlooked and the simulated
results hardly transfer to real hardware. Either it is unsuccessful in practice
because the physics is over-simplified and hardware limitations are ignored, or
regularity is not guaranteed, and unexpected hazardous motions can occur. This
paper presents a reinforcement learning framework capable of learning robust
standing push recovery for bipedal robots that smoothly transfer to reality,
providing only instantaneous proprioceptive observations. By combining original
termination conditions and policy smoothness conditioning, we achieve stable
learning, sim-to-real transfer and safety using a policy without memory nor
explicit history. Reward engineering is then used to give insights into how to
keep balance. We demonstrate its performance in reality on the lower-limb
medical exoskeleton Atalante
New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates
In voting contexts, some new candidates may show up in the course of the
process. In this case, we may want to determine which of the initial candidates
are possible winners, given that a fixed number of new candidates will be
added. We give a computational study of this problem, focusing on scoring
rules, and we provide a formal comparison with related problems such as control
via adding candidates or cloning.Comment: 34 page
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