Multispectral Spatial Characterization: Application to Mitosis Detection in Breast Cancer Histopathology

Apr 15, 2013

H. Irshad, A. Gouaillard, L. Roux, D. Racoceanu

Accurate detection of mitosis plays a critical role in breast cancer histopathology. Manual detection and counting of mitosis is tedious and subject to considerable inter- and intra-reader variations. Multispectral imaging is a recent medical imaging technology, proven successful in increasing the segmentation accuracy in other fields. This study aims at improving the accuracy of mitosis detection by developing a specific solution using multispectral and multifocal imaging of breast cancer histopathological data. We propose to enable clinical routine-compliant quality of mitosis discrimination from other objects. The proposed framework includes comprehensive analysis of spectral bands and z-stack focus planes, detection of expected mitotic regions (candidates) in selected focus planes and spectral bands, computation of multispectral spatial features for each candidate, selection of multispectral spatial features and a study of different state-of-the-art classification methods for candidates classification as mitotic or non mitotic figures. This framework has been evaluated on MITOS multispectral medical dataset and achieved 60% detection rate and 57% F-Measure. Our results indicate that multispectral spatial features have more information for mitosis classification in comparison with white spectral band features, being therefore a very promising exploration area to improve the quality of the diagnosis assistance in histopathology.
Apr 15, 2013

H. Irshad, A. Gouaillard, L. Roux, D. Racoceanu

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Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier work has focused on learning only the bandwidth of the kernel (i.e., a scalar multiplicative factor). In this paper, we propose to learn a full Euclidean metric through an expectation-minimization (EM) procedure, which can be seen as an unsupervised counterpart to neighbourhood component analysis (NCA). In order to avoid overfitting with a fully nonparametric density estimator in high dimensions, we also consider a semi-parametric Gaussian-Parzen density model, where some of the variables are modelled through a jointly Gaussian density, while others are modelled through Parzen windows. For these two models, EM leads to simple closed-form updates based on matrix inversions and eigenvalue decompositions. We show empirically that our method leads to density estimators with higher test-likelihoods than natural competing methods, and that the metrics may be used within most unsupervised learning techniques that rely on such metrics, such as spectral clustering or manifold learning methods. Finally, we present a stochastic approximation scheme which allows for the use of this method in a large-scale setting.

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A comparative study of counterfactual estimators

May 02, 2017

Thomas Nedelec, Nicolas Le Roux, Vianney Perchet

We provide a comparative study of several widely used off-policy estimators (Empirical Average, Basic Importance Sampling and Normalized Importance Sampling), detailing the different regimes where they are individually suboptimal. We then exhibit properties optimal estimators should possess. In the case where examples have been gathered using multiple policies, we show that fused estimators dominate basic ones but can still be improved.
May 02, 2017

Thomas Nedelec, Nicolas Le Roux, Vianney Perchet

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Distributional reinforcement learning with linear function approximation

Feb 08, 2019

Marc G. Bellemare, Nicolas Le Roux, Pablo Samuel Castro, Subhodeep Moitra

Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cram\'er distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cram\'er-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the model's prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cram\'er-based distributional methods may perform worse than directly approximating the value function.
Feb 08, 2019

Marc G. Bellemare, Nicolas Le Roux, Pablo Samuel Castro, Subhodeep Moitra

* Proceedings of AISTATS 2019

* To appear

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Phasebook and Friends: Leveraging Discrete Representations for Source Separation

Oct 02, 2018

Jonathan Le Roux, Gordon Wichern, Shinji Watanabe, Andy Sarroff, John R. Hershey

Deep learning based speech enhancement and source separation systems have recently reached unprecedented levels of quality, to the point that performance is reaching a new ceiling. Most systems rely on estimating the magnitude of a target source by estimating a real-valued mask to be applied to a time-frequency representation of the mixture signal. A limiting factor in such approaches is a lack of phase estimation: the phase of the mixture is most often used when reconstructing the estimated time-domain signal. Here, we propose `MagBook', `phasebook', and `Combook', three new types of layers based on discrete representations that can be used to estimate complex time-frequency masks. MagBook layers extend classical sigmoidal units and a recently introduced convex softmax activation for mask-based magnitude estimation. Phasebook layers use a similar structure to give an estimate of the phase mask without suffering from phase wrapping issues. Combook layers are an alternative to the MagBook-Phasebook combination that directly estimate complex masks. We present various training and inference regimes involving these representations, and explain in particular how to include them in an end-to-end learning framework. We also present an oracle study to assess upper bounds on performance for various types of masks using discrete phase representations. We evaluate the proposed methods on the wsj0-2mix dataset, a well-studied corpus for single-channel speaker-independent speaker separation, matching the performance of state-of-the-art mask-based approaches without requiring additional phase reconstruction steps.
Oct 02, 2018

Jonathan Le Roux, Gordon Wichern, Shinji Watanabe, Andy Sarroff, John R. Hershey

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The Value Function Polytope in Reinforcement Learning

Feb 15, 2019

Robert Dadashi, Adrien Ali Taïga, Nicolas Le Roux, Dale Schuurmans, Marc G. Bellemare

We establish geometric and topological properties of the space of value functions in finite state-action Markov decision processes. Our main contribution is the characterization of the nature of its shape: a general polytope (Aigner et al., 2010). To demonstrate this result, we exhibit several properties of the structural relationship between policies and value functions including the line theorem, which shows that the value functions of policies constrained on all but one state describe a line segment. Finally, we use this novel perspective to introduce visualizations to enhance the understanding of the dynamics of reinforcement learning algorithms.
Feb 15, 2019

Robert Dadashi, Adrien Ali Taïga, Nicolas Le Roux, Dale Schuurmans, Marc G. Bellemare

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Cycle-consistency training for end-to-end speech recognition

Nov 02, 2018

Takaaki Hori, Ramon Astudillo, Tomoki Hayashi, Yu Zhang, Shinji Watanabe, Jonathan Le Roux

This paper presents a method to train end-to-end automatic speech recognition (ASR) models using unpaired data. Although the end-to-end approach can eliminate the need for expert knowledge such as pronunciation dictionaries to build ASR systems, it still requires a large amount of paired data, i.e., speech utterances and their transcriptions. Cycle-consistency losses have been recently proposed as a way to mitigate the problem of limited paired data. These approaches compose a reverse operation with a given transformation, e.g., text-to-speech (TTS) with ASR, to build a loss that only requires unsupervised data, speech in this example. Applying cycle consistency to ASR models is not trivial since fundamental information, such as speaker traits, are lost in the intermediate text bottleneck. To solve this problem, this work presents a loss that is based on the speech encoder state sequence instead of the raw speech signal. This is achieved by training a Text-To-Encoder model and defining a loss based on the encoder reconstruction error. Experimental results on the LibriSpeech corpus show that the proposed cycle-consistency training reduced the word error rate by 14.7% from an initial model trained with 100-hour paired data, using an additional 360 hours of audio data without transcriptions. We also investigate the use of text-only data mainly for language modeling to further improve the performance in the unpaired data training scenario.
Nov 02, 2018

Takaaki Hori, Ramon Astudillo, Tomoki Hayashi, Yu Zhang, Shinji Watanabe, Jonathan Le Roux

* Submitted to ICASSP'19

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Reducing the variance in online optimization by transporting past gradients

Jun 18, 2019

Sébastien M. R. Arnold, Pierre-Antoine Manzagol, Reza Babanezhad, Ioannis Mitliagkas, Nicolas Le Roux

Most stochastic optimization methods use gradients once before discarding them. While variance reduction methods have shown that reusing past gradients can be beneficial when there is a finite number of datapoints, they do not easily extend to the online setting. One issue is the staleness due to using past gradients. We propose to correct this staleness using the idea of implicit gradient transport (IGT) which transforms gradients computed at previous iterates into gradients evaluated at the current iterate without using the Hessian explicitly. In addition to reducing the variance and bias of our updates over time, IGT can be used as a drop-in replacement for the gradient estimate in a number of well-understood methods such as heavy ball or Adam. We show experimentally that it achieves state-of-the-art results on a wide range of architectures and benchmarks. Additionally, the IGT gradient estimator yields the optimal asymptotic convergence rate for online stochastic optimization in the restricted setting where the Hessians of all component functions are equal.
Jun 18, 2019

Sébastien M. R. Arnold, Pierre-Antoine Manzagol, Reza Babanezhad, Ioannis Mitliagkas, Nicolas Le Roux

* Open-source implementation available at: https://github.com/seba-1511/igt.pth

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Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units

Jan 28, 2014

Guido F. Montúfar

We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever and Hinton, 2008; Le Roux and Bengio, 2008, 2010; Mont\'ufar and Ay, 2011) to units with arbitrary finite state spaces, and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a $q$-ary deep belief network with $L\geq 2+\frac{q^{\lceil m-\delta \rceil}-1}{q-1}$ layers of width $n \leq m + \log_q(m) + 1$ for some $m\in \mathbb{N}$ can approximate any probability distribution on $\{0,1,\ldots,q-1\}^n$ without exceeding a Kullback-Leibler divergence of $\delta$. Our analysis covers discrete restricted Boltzmann machines and na\"ive Bayes models as special cases.
Jan 28, 2014

Guido F. Montúfar

* 19 pages, 5 figures, 1 table

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Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines

Jul 26, 2010

Guido Montufar, Nihat Ay

We improve recently published results about resources of Restricted Boltzmann Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal Approximators. We show that any distribution p on the set of binary vectors of length n can be arbitrarily well approximated by an RBM with k-1 hidden units, where k is the minimal number of pairs of binary vectors differing in only one entry such that their union contains the support set of p. In important cases this number is half of the cardinality of the support set of p. We construct a DBN with 2^n/2(n-b), b ~ log(n), hidden layers of width n that is capable of approximating any distribution on {0,1}^n arbitrarily well. This confirms a conjecture presented by Le Roux and Bengio 2010.
Jul 26, 2010

Guido Montufar, Nihat Ay

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We evaluate natural gradient, an algorithm originally proposed in Amari (1997), for learning deep models. The contributions of this paper are as follows. We show the connection between natural gradient and three other recently proposed methods for training deep models: Hessian-Free (Martens, 2010), Krylov Subspace Descent (Vinyals and Povey, 2012) and TONGA (Le Roux et al., 2008). We describe how one can use unlabeled data to improve the generalization error obtained by natural gradient and empirically evaluate the robustness of the algorithm to the ordering of the training set compared to stochastic gradient descent. Finally we extend natural gradient to incorporate second order information alongside the manifold information and provide a benchmark of the new algorithm using a truncated Newton approach for inverting the metric matrix instead of using a diagonal approximation of it.

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