arXiv subjects

Guillaume Rabusseau

Publications and source records attributed to Guillaume Rabusseau.

72 records · Page 4Linked to original sources

arXiv2020

Representation of Reinforcement Learning Policies in Reproducing Kernel Hilbert Spaces

We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of the reconstructed policy. Such guarantees are typically lacking in black-box models, but are very desirable in tasks requiring stability. We conduct several experiments on classic RL domains. The results confirm that the policies can be robustly embedded in a low-dimensional space while the embedded policy incurs almost no decrease in return.

cs.LG↗

arXiv2020

Laplacian Change Point Detection for Dynamic Graphs

Dynamic and temporal graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion identification in network systems, detection of ecosystem disturbances and detection of epidemic outbreaks. In this paper, we focus on change point detection in dynamic graphs and address two main challenges associated with this problem: I) how to compare graph snapshots across time, II) how to capture temporal dependencies. To solve the above challenges, we propose Laplacian Anomaly Detection (LAD) which uses the spectrum of the Laplacian matrix of the graph structure at each snapshot to obtain low dimensional embeddings. LAD explicitly models short term and long term dependencies by applying two sliding windows. In synthetic experiments, LAD outperforms the state-of-the-art method. We also evaluate our method on three real dynamic networks: UCI message network, US senate co-sponsorship network and Canadian bill voting network. In all three datasets, we demonstrate that our method can more effectively identify anomalous time points according to significant real world events.

cs.LG↗

arXiv2020

Tensorized Random Projections

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose two tensorized random projection maps relying on the tensor train~(TT) and CP decomposition format, respectively. The two maps offer very low memory requirements and can be applied efficiently when the inputs are low rank tensors given in the CP or TT format. Our theoretical analysis shows that the dense Gaussian matrix in JLT can be replaced by a low-rank tensor implicitly represented in compressed form with random factors, while still approximately preserving the Euclidean distance of the projected inputs. In addition, our results reveal that the TT format is substantially superior to CP in terms of the size of the random projection needed to achieve the same distortion ratio. Experiments on synthetic data validate our theoretical analysis and demonstrate the superiority of the TT decomposition.

cs.LG↗

arXiv2020

RandomNet: Towards Fully Automatic Neural Architecture Design for Multimodal Learning

Almost all neural architecture search methods are evaluated in terms of performance (i.e. test accuracy) of the model structures that it finds. Should it be the only metric for a good autoML approach? To examine aspects beyond performance, we propose a set of criteria aimed at evaluating the core of autoML problem: the amount of human intervention required to deploy these methods into real world scenarios. Based on our proposed evaluation checklist, we study the effectiveness of a random search strategy for fully automated multimodal neural architecture search. Compared to traditional methods that rely on manually crafted feature extractors, our method selects each modality from a large search space with minimal human supervision. We show that our proposed random search strategy performs close to the state of the art on the AV-MNIST dataset while meeting the desirable characteristics for a fully automated design process.

cs.LG↗

arXiv2019

Efficient Planning under Partial Observability with Unnormalized Q Functions and Spectral Learning

Learning and planning in partially-observable domains is one of the most difficult problems in reinforcement learning. Traditional methods consider these two problems as independent, resulting in a classical two-stage paradigm: first learn the environment dynamics and then plan accordingly. This approach, however, disconnects the two problems and can consequently lead to algorithms that are sample inefficient and time consuming. In this paper, we propose a novel algorithm that combines learning and planning together. Our algorithm is closely related to the spectral learning algorithm for predicitive state representations and offers appealing theoretical guarantees and time complexity. We empirically show on two domains that our approach is more sample and time efficient compared to classical methods.

cs.AI↗

arXiv2019

Neural Architecture Search for Class-incremental Learning

In class-incremental learning, a model learns continuously from a sequential data stream in which new classes occur. Existing methods often rely on static architectures that are manually crafted. These methods can be prone to capacity saturation because a neural network's ability to generalize to new concepts is limited by its fixed capacity. To understand how to expand a continual learner, we focus on the neural architecture design problem in the context of class-incremental learning: at each time step, the learner must optimize its performance on all classes observed so far by selecting the most competitive neural architecture. To tackle this problem, we propose Continual Neural Architecture Search (CNAS): an autoML approach that takes advantage of the sequential nature of class-incremental learning to efficiently and adaptively identify strong architectures in a continual learning setting. We employ a task network to perform the classification task and a reinforcement learning agent as the meta-controller for architecture search. In addition, we apply network transformations to transfer weights from previous learning step and to reduce the size of the architecture search space, thus saving a large amount of computational resources. We evaluate CNAS on the CIFAR-100 dataset under varied incremental learning scenarios with limited computational power (1 GPU). Experimental results demonstrate that CNAS outperforms architectures that are optimized for the entire dataset. In addition, CNAS is at least an order of magnitude more efficient than naively using existing autoML methods.

cs.LG↗

arXiv2019

Connecting Weighted Automata and Recurrent Neural Networks through Spectral Learning

In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions are expressively equivalent. Motivated by this result, we build upon a recent extension of the spectral learning algorithm to vector-valued WFAs and propose the first provable learning algorithm for linear 2-RNNs defined over sequences of continuous input vectors. This algorithm relies on estimating low rank sub-blocks of the so-called Hankel tensor, from which the parameters of a linear 2-RNN can be provably recovered. The performances of the proposed method are assessed in a simulation study.

cs.LG↗

arXiv2019

On overfitting and asymptotic bias in batch reinforcement learning with partial observability

This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability. Our theoretical analysis formally characterizes that while potentially increasing the asymptotic bias, a smaller state representation decreases the risk of overfitting. This analysis relies on expressing the quality of a state representation by bounding L1 error terms of the associated belief states. Theoretical results are empirically illustrated when the state representation is a truncated history of observations, both on synthetic POMDPs and on a large-scale POMDP in the context of smartgrids, with real-world data. Finally, similarly to known results in the fully observable setting, we also briefly discuss and empirically illustrate how using function approximators and adapting the discount factor may enhance the tradeoff between asymptotic bias and overfitting in the partially observable context.

stat.ML↗

arXiv2018

Clustering-Oriented Representation Learning with Attractive-Repulsive Loss

The standard loss function used to train neural network classifiers, categorical cross-entropy (CCE), seeks to maximize accuracy on the training data; building useful representations is not a necessary byproduct of this objective. In this work, we propose clustering-oriented representation learning (COREL) as an alternative to CCE in the context of a generalized attractive-repulsive loss framework. COREL has the consequence of building latent representations that collectively exhibit the quality of natural clustering within the latent space of the final hidden layer, according to a predefined similarity function. Despite being simple to implement, COREL variants outperform or perform equivalently to CCE in a variety of scenarios, including image and news article classification using both feed-forward and convolutional neural networks. Analysis of the latent spaces created with different similarity functions facilitates insights on the different use cases COREL variants can satisfy, where the Cosine-COREL variant makes a consistently clusterable latent space, while Gaussian-COREL consistently obtains better classification accuracy than CCE.

cs.LG↗

arXiv2018

Learning Graph Weighted Models on Pictures

Graph Weighted Models (GWMs) have recently been proposed as a natural generalization of weighted automata over strings and trees to arbitrary families of labeled graphs (and hypergraphs). A GWM generically associates a labeled graph with a tensor network and computes a value by successive contractions directed by its edges. In this paper, we consider the problem of learning GWMs defined over the graph family of pictures (or 2-dimensional words). As a proof of concept, we consider regression and classification tasks over the simple Bars & Stripes and Shifting Bits picture languages and provide an experimental study investigating whether these languages can be learned in the form of a GWM from positive and negative examples using gradient-based methods. Our results suggest that this is indeed possible and that investigating the use of gradient-based methods to learn picture series and functions computed by GWMs over other families of graphs could be a fruitful direction.

cs.FL↗

arXiv2018

Tensor Regression Networks with various Low-Rank Tensor Approximations

Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years, tensor regression networks have been investigated from the perspective of their compressive power, however, the regularization effect of enforcing low-rank tensor structure has not been investigated enough. We study tensor regression networks using various low-rank tensor approximations, aiming to compare the compressive and regularization power of different low-rank constraints. We evaluate the compressive and regularization performances of the proposed model with both deep and shallow convolutional neural networks. The outcome of our experiment suggests the superiority of Global Average Pooling Layer over Tensor Regression Layer when applied to deep convolutional neural network with CIFAR-10 dataset. On the contrary, shallow convolutional neural networks with tensor regression layer and dropout achieved lower test error than both Global Average Pooling and fully-connected layer with dropout function when trained with a small number of samples.

cs.LG↗

arXiv2018

Hierarchical Methods of Moments

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to model misspecification. In this paper we present a hierarchical approach to methods of moments to circumvent such limitations. Our method is based on replacing the tensor decomposition step used in previous algorithms with approximate joint diagonalization. Experiments on topic modeling show that our method outperforms previous tensor decomposition methods in terms of speed and model quality.

stat.ML↗

arXiv2018

Sequential Coordination of Deep Models for Learning Visual Arithmetic

Achieving machine intelligence requires a smooth integration of perception and reasoning, yet models developed to date tend to specialize in one or the other; sophisticated manipulation of symbols acquired from rich perceptual spaces has so far proved elusive. Consider a visual arithmetic task, where the goal is to carry out simple arithmetical algorithms on digits presented under natural conditions (e.g. hand-written, placed randomly). We propose a two-tiered architecture for tackling this problem. The lower tier consists of a heterogeneous collection of information processing modules, which can include pre-trained deep neural networks for locating and extracting characters from the image, as well as modules performing symbolic transformations on the representations extracted by perception. The higher tier consists of a controller, trained using reinforcement learning, which coordinates the modules in order to solve the high-level task. For instance, the controller may learn in what contexts to execute the perceptual networks and what symbolic transformations to apply to their outputs. The resulting model is able to solve a variety of tasks in the visual arithmetic domain, and has several advantages over standard, architecturally homogeneous feedforward networks including improved sample efficiency.

cs.LG↗

arXiv2017

Neural Network Based Nonlinear Weighted Finite Automata

Weighted finite automata (WFA) can expressively model functions defined over strings but are inherently linear models. Given the recent successes of nonlinear models in machine learning, it is natural to wonder whether ex-tending WFA to the nonlinear setting would be beneficial. In this paper, we propose a novel model of neural network based nonlinearWFA model (NL-WFA) along with a learning algorithm. Our learning algorithm is inspired by the spectral learning algorithm for WFAand relies on a nonlinear decomposition of the so-called Hankel matrix, by means of an auto-encoder network. The expressive power of NL-WFA and the proposed learning algorithm are assessed on both synthetic and real-world data, showing that NL-WFA can lead to smaller model sizes and infer complex grammatical structures from data.

cs.FL↗

arXiv2016

Higher-Order Low-Rank Regression

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension is also presented. Experiments on synthetic and real data show that HOLRR outperforms multivariate and multilinear regression methods and is considerably faster than existing tensor methods.

cs.LG↗

arXiv2015

Low-Rank Approximation of Weighted Tree Automata

We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.

cs.LG↗

arXiv2014

Recognizable Series on Hypergraphs

We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family is said to be recognizable if there exists a HWM that computes it. This model generalizes the notion of rational series on strings and trees. We prove some properties of the model and study at which conditions finite support series are recognizable.

cs.FL↗

arXiv2014

Learning Negative Mixture Models by Tensor Decompositions

This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability distributions on strings, a representation which occurs naturally in spectral learning, can be computed by a negative mixture of at most two probabilistic automata (or HMMs). (ii) We propose a method to estimate the parameters of negative mixture models having a specific tensor structure in their low order observable moments. Building upon a recent paper on tensor decompositions for learning latent variable models, we extend this work to the broader setting of tensors having a symmetric decomposition with positive and negative weights. We introduce a generalization of the tensor power method for complex valued tensors, and establish theoretical convergence guarantees. (iii) We show how our approach applies to negative Gaussian mixture models, for which we provide some experiments.

cs.LG↗