pwc-archive/papers-with-abstracts huggingface dataset:
A Sparse Interactive Model for Matrix Completion with Side Information
Authors: Jin Lu, Guannan Liang, Jiangwen Sun, Jinbo Bi
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Matrix Completion

Matrix completion methods can benefit from side information besides the partially observed matrix. The use of side features describing the row and column entities of a matrix has been shown to reduce the sample complexity for completing the matrix. We propose a novel sparse formulation that explicitly models the interaction between the row and column side features to approximate the matrix entries. Unlike early methods, this model does not require the low-rank condition on the model parameter matrix. We prove that when the side features can span the latent feature space of the matrix to be recovered, the number of observed entries needed for an exact recovery is $O(\log N)$ where $N$ is the size of the matrix. When the side features are corrupted latent features of the matrix with a small perturbation, our method can achieve an $\epsilon$-recovery with $O(\log N)$ sample complexity, and maintains a $\O(N^{3/2})$ rate similar to classfic methods with no side information. An efficient linearized Lagrangian algorithm is developed with a strong guarantee of convergence. Empirical results show that our approach outperforms three state-of-the-art methods both in simulations and on real world datasets.
Agnostic Estimation for Misspecified Phase Retrieval Models
Authors: Matey Neykov, Zhaoran Wang, Han Liu
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Retrieval

The goal of noisy high-dimensional phase retrieval is to estimate an $s$-sparse parameter $\boldsymbol{\beta}^*\in \mathbb{R}^d$ from $n$ realizations of the model $Y = (\boldsymbol{X}^{\top} \boldsymbol{\beta}^*)^2 + \varepsilon$. Based on this model, we propose a significant semi-parametric generalization called misspecified phase retrieval (MPR), in which $Y = f(\boldsymbol{X}^{\top}\boldsymbol{\beta}^*, \varepsilon)$ with unknown $f$ and $\operatorname{Cov}(Y, (\boldsymbol{X}^{\top}\boldsymbol{\beta}^*)^2) > 0$. For example, MPR encompasses $Y = h(|\boldsymbol{X}^{\top} \boldsymbol{\beta}^*|) + \varepsilon$ with increasing $h$ as a special case. Despite the generality of the MPR model, it eludes the reach of most existing semi-parametric estimators. In this paper, we propose an estimation procedure, which consists of solving a cascade of two convex programs and provably recovers the direction of $\boldsymbol{\beta}^*$. Our theory is backed up by thorough numerical results.
Linear Relaxations for Finding Diverse Elements in Metric Spaces
Authors: Aditya Bhaskara, Mehrdad Ghadiri, Vahab Mirrokni, Ola Svensson
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Data Summarization, Diversity, feature selection, Recommendation Systems

Choosing a diverse subset of a large collection of points in a metric space is a fundamental problem, with applications in feature selection, recommender systems, web search, data summarization, etc. Various notions of diversity have been proposed, tailored to different applications. The general algorithmic goal is to find a subset of points that maximize diversity, while obeying a cardinality (or more generally, matroid) constraint.  The goal of this paper is to develop a novel linear programming (LP) framework that allows us to design approximation algorithms for such problems. We study an objective known as {\em sum-min} diversity, which is known to be effective in many applications, and give the first constant factor approximation algorithm. Our LP framework allows us to easily incorporate additional constraints, as well as secondary objectives. We also prove a hardness result for two natural diversity objectives, under the  so-called {\em planted clique} assumption. Finally, we study the empirical performance of our algorithm on several standard datasets. We first study the approximation quality of the algorithm by comparing with the LP objective. Then, we compare the quality of the solutions produced by our method with other popular diversity maximization algorithms.
Bayesian Optimization with Robust Bayesian Neural Networks
Authors: Jost Tobias Springenberg, Aaron Klein, Stefan Falkner, Frank Hutter
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Bayesian Optimization, Deep Reinforcement Learning, Hyperparameter Optimization, Reinforcement Learning, Reinforcement Learning (RL)

Bayesian optimization is a prominent method for optimizing expensive to evaluate black-box functions that is prominently applied to tuning the hyperparameters of machine learning algorithms. Despite its successes, the prototypical Bayesian optimization approach - using Gaussian process models - does not scale well to either many hyperparameters or many function evaluations. Attacking this lack of scalability and flexibility is thus one of the key challenges of the field. We present a general approach for using flexible parametric models (neural networks) for Bayesian optimization, staying as close to a truly Bayesian treatment as possible. We obtain scalability through stochastic gradient Hamiltonian Monte Carlo, whose robustness we improve via a scale adaptation. Experiments including multi-task Bayesian optimization with 21 tasks, parallel optimization of deep neural networks and deep reinforcement learning show the power and flexibility of this approach.
One-vs-Each Approximation to Softmax for Scalable Estimation of Probabilities
Authors: Michalis Titsias Rc Aueb
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: General Classification, Language Modeling, Language Modelling, Recommendation Systems, Stochastic Optimization

The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation systems. However, softmax estimation is very expensive for large scale inference because of the high cost associated with computing the normalizing constant. Here, we introduce an efficient approximation to softmax probabilities which takes the form of a rigorous lower bound on the exact probability. This bound is expressed as a product over pairwise probabilities and it leads to scalable estimation based on stochastic optimization. It allows us to perform doubly stochastic estimation by subsampling both training instances and class labels. We show that the new bound has interesting theoretical properties and we demonstrate its use in classification problems.
Mapping Estimation for Discrete Optimal Transport
Authors: Michaël Perrot, Nicolas Courty, Rémi Flamary, Amaury Habrard
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Domain Adaptation

We are interested in the computation of the transport map of an Optimal Transport problem. Most of the computational approaches of Optimal Transport use the Kantorovich relaxation of the problem to learn a probabilistic coupling $\mgamma$ but do not address the problem of learning the underlying transport map $\funcT$ linked to the original Monge problem. Consequently, it lowers the potential usage of such methods in contexts where out-of-samples computations are mandatory. In this paper we propose a new way to jointly learn the coupling and an approximation of the transport map. We use a jointly convex formulation which can be efficiently optimized. Additionally, jointly learning the coupling and the transport map allows to smooth the result of the Optimal Transport and generalize it to out-of-samples examples. Empirically, we show the interest and the relevance of our method in two tasks: domain adaptation and image editing.
Protein contact prediction from amino acid co-evolution using convolutional networks for graph-valued images
Authors: Vladimir Golkov, Marcin J. Skwark, Antonij Golkov, Alexey Dosovitskiy, Thomas Brox, Jens Meiler, Daniel Cremers
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12

Proteins are the "building blocks of life", the most abundant organic molecules, and the central focus of most areas of biomedicine. Protein structure is strongly related to protein function, thus structure prediction is a crucial task on the way to solve many biological questions. A contact map is a compact representation of the three-dimensional structure of a protein via the pairwise contacts between the amino acid constituting the protein. We use a convolutional network to calculate protein contact maps from inferred statistical coupling between positions in the protein sequence. The input to the network has an image-like structure amenable to convolutions, but every "pixel" instead of color channels contains a bipartite undirected edge-weighted graph. We propose several methods for treating such "graph-valued images" in a convolutional network. The proposed method outperforms state-of-the-art methods by a large margin. It also allows for a great flexibility with regard to the input data, which makes it useful for studying a wide range of problems.
Linear Feature Encoding for Reinforcement Learning
Authors: Zhao Song, Ronald E. Parr, Xuejun Liao, Lawrence Carin
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Deep Reinforcement Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Feature construction is of vital importance in reinforcement learning, as the quality of a value function or policy is largely determined by the corresponding features. The recent successes of deep reinforcement learning (RL) only increase the importance of understanding feature construction. Typical deep RL approaches use a linear output layer, which means that deep RL can be interpreted as a feature construction/encoding network followed by linear value function approximation. This paper develops and evaluates a theory of linear feature encoding. We extend theoretical results on feature quality for linear value function approximation from the uncontrolled case to the controlled case. We then develop a supervised linear feature encoding method that is motivated by insights from linear value function approximation theory, as well as empirical successes from deep RL. The resulting encoder is a surprisingly effective method for linear value function approximation using raw images as inputs.
Completely random measures for modelling block-structured sparse networks
Authors: Tue Herlau, Mikkel N. Schmidt, Morten Mørup
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12

Statistical methods for network data often parameterize the edge-probability by attributing latent traits such as block structure to the vertices and assume exchangeability in the sense of the Aldous-Hoover representation theorem. These assumptions are however incompatible with traits found in real-world networks such as a power-law degree-distribution. Recently, Caron & Fox (2014) proposed the use of a different notion of exchangeability after Kallenberg (2005) and obtained a network model which permits edge-inhomogeneity, such as a power-law degree-distribution whilst retaining desirable statistical properties. However, this model does not capture latent vertex traits such as block-structure. In this work we re-introduce the use of block-structure for network models obeying Kallenberg’s notion of exchangeability and thereby obtain a collapsed model which both admits the inference of block-structure and edge inhomogeneity. We derive a simple expression for the likelihood and an efficient sampling method. The obtained model is not significantly more difficult to implement than existing approaches to block-modelling and performs well on real network datasets.
Sparse Support Recovery with Non-smooth Loss Functions
Authors: Kévin Degraux, Gabriel Peyré, Jalal Fadili, Laurent Jacques
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: compressed sensing

In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of $\ell_1$ and $\ell_\infty$ losses, and contrast them with the usual $\ell_2$ loss.While these losses are routinely used to account for either sparse ($\ell_1$ loss) or uniform ($\ell_\infty$ loss) noise models, a theoretical analysis of their performance is still lacking. In this article, we extend the existing theory from the smooth $\ell_2$ case to these non-smooth cases. We derive a sharp condition which ensures that the support of the vector to recover is stable to small additive noise in the observations, as long as the loss constraint size is tuned proportionally to the noise level. A distinctive feature of our theory is that it also explains what happens when the support is unstable. While the support is not stable anymore, we identify an "extended support" and show that this extended support is stable to small additive noise. To exemplify the usefulness of our theory, we give a detailed numerical analysis of the support stability/instability of compressed sensing recovery with these different losses. This highlights different parameter regimes, ranging from total support stability to progressively increasing support instability.
Neurons Equipped with Intrinsic Plasticity Learn Stimulus Intensity Statistics
Authors: Travis Monk, Cristina Savin, Jörg Lücke
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12

Experience constantly shapes neural circuits through a variety of plasticity mechanisms. While the functional roles of some plasticity mechanisms are well-understood, it remains unclear how changes in neural excitability contribute to learning. Here, we develop a normative interpretation of intrinsic plasticity (IP) as a key component of unsupervised learning. We introduce a novel generative mixture model that accounts for the class-specific statistics of stimulus intensities, and we derive a neural circuit that learns the input classes and their intensities. We will analytically show that inference and learning for our generative model can be achieved by a neural circuit with intensity-sensitive neurons equipped with a specific form of IP. Numerical experiments verify our analytical derivations and show robust behavior for artificial and natural stimuli. Our results link IP to non-trivial input statistics, in particular the statistics of stimulus intensities for classes to which a neuron is sensitive. More generally, our work paves the way toward new classification algorithms that are robust to intensity variations.
Adaptive Smoothed Online Multi-Task Learning
Authors: Keerthiram Murugesan, Hanxiao Liu, Jaime Carbonell, Yiming Yang
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Multi-Task Learning

This paper addresses the challenge of jointly learning both the per-task model parameters and the inter-task relationships in a multi-task online learning setting. The proposed algorithm features probabilistic interpretation, efficient updating rules and flexible modulation on whether learners focus on their specific task or on jointly address all tasks.  The paper also proves a sub-linear regret bound as compared to the best linear predictor in hindsight. Experiments over three multi-task learning benchmark datasets show advantageous performance of the proposed approach over several state-of-the-art online multi-task learning baselines.
beta-risk: a New Surrogate Risk for Learning from Weakly Labeled Data
Authors: Valentina Zantedeschi, Rémi Emonet, Marc Sebban
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12

During the past few years, the machine learning community has paid attention to developping new methods for learning from weakly labeled data. This field covers different settings like semi-supervised learning, learning with label proportions, multi-instance learning, noise-tolerant learning, etc. This paper presents a generic framework to deal with these weakly labeled scenarios. We introduce the beta-risk as a generalized formulation of the standard empirical risk based on surrogate margin-based loss functions. This risk allows us to express the reliability on the labels and to derive different kinds of learning algorithms. We specifically focus on SVMs and propose a soft margin beta-svm algorithm  which behaves better that the state of the art.
Learning Additive Exponential Family Graphical Models via \ell_{2,1}-norm Regularized M-Estimation
Authors: Xiaotong Yuan, Ping Li, Tong Zhang, Qingshan Liu, Guangcan Liu
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12

We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two $\ell_{2,1}$-norm regularized maximum likelihood estimators to learn the model parameters from i.i.d. samples. The first one is a joint MLE estimator which estimates all the parameters simultaneously. The second one is a node-wise conditional MLE estimator which estimates the parameters for each node individually. For both estimators, statistical analysis shows that under mild conditions the extra flexibility gained by the additive exponential family models comes at almost no cost of statistical efficiency. A Monte-Carlo approximation method is developed to efficiently optimize the proposed estimators. The advantages of our estimators over Gaussian graphical models and Nonparanormal estimators are demonstrated on synthetic and real data sets.
Fast recovery from a union of subspaces
Authors: Chinmay Hegde, Piotr Indyk, Ludwig Schmidt
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Compressive Sensing

We address the problem of recovering a high-dimensional but structured vector from linear observations in a general setting where the vector can come from an arbitrary union of subspaces. This setup includes well-studied problems such as compressive sensing and low-rank matrix recovery. We show how to design more efficient algorithms for the union-of subspace recovery problem by using *approximate* projections. Instantiating our general framework for the low-rank matrix recovery problem gives the fastest provable running time for an algorithm with optimal sample complexity. Moreover, we give fast approximate projections for 2D histograms, another well-studied low-dimensional model of data. We complement our theoretical results with experiments demonstrating that our framework also leads to improved time and sample complexity empirically.
Incremental Variational Sparse Gaussian Process Regression
Authors: Ching-An Cheng, Byron Boots
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: GPR, Incremental Learning, regression

Recent work on scaling up Gaussian process regression (GPR) to large datasets has primarily focused on sparse GPR, which leverages a small set of basis functions to approximate the full Gaussian process during inference.  However, the majority of these approaches are batch methods that operate on the entire training dataset at once, precluding the use of datasets that are streaming or too large to fit into memory. Although previous work has considered incrementally solving variational sparse GPR, most algorithms fail to update the basis functions and therefore perform suboptimally. We propose a novel incremental learning algorithm for variational sparse GPR based on stochastic mirror ascent of probability densities in reproducing kernel Hilbert space. This new formulation allows our algorithm to update basis functions online in accordance with the manifold structure of probability densities for fast convergence. We conduct several experiments and show that our proposed approach achieves better empirical performance in terms of prediction error than  the recent state-of-the-art incremental solutions to variational sparse GPR.
An urn model for majority voting in classification ensembles
Authors: Victor Soto, Alberto Suárez, Gonzalo Martinez-Muñoz
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Classification, General Classification, Prediction

In this work we analyze the class prediction of parallel randomized ensembles by majority voting as an urn model. For a given test instance, the ensemble can be viewed as an urn of marbles of different colors. A marble represents an individual classifier. Its color represents the class label prediction of the corresponding classifier. The sequential querying of classifiers in the ensemble can be seen as draws without replacement from the urn. An analysis of this classical urn model based on the hypergeometric distribution makes it possible to estimate the confidence on the outcome of majority voting when only a fraction of the individual predictions is known. These estimates can be used to speed up the prediction by the ensemble. Specifically, the aggregation of votes can be halted when the confidence in the final prediction is sufficiently high. If one assumes a uniform prior for the distribution of possible votes the analysis is shown to be equivalent to a previous one based on Dirichlet distributions. The advantage of the current approach is that prior knowledge on the possible vote outcomes can be readily incorporated in a Bayesian framework. We show how incorporating this type of problem-specific knowledge into the statistical analysis of majority voting leads to faster classification by the ensemble and allows us to estimate the expected average speed-up beforehand.
Fast and accurate spike sorting of high-channel count probes with KiloSort
Authors: Marius Pachitariu, Nicholas A. Steinmetz, Shabnam N. Kadir, Matteo Carandini, Kenneth D. Harris
Date: 2016-12-01 00:00:00
Proceeding: NeurIPS 2016 12
Tasks: Clustering, Spike Sorting, Template Matching

New silicon technology is enabling large-scale electrophysiological recordings in vivo from hundreds to thousands of channels. Interpreting these recordings requires scalable and accurate automated methods for spike sorting, which should minimize the time required for manual curation of the results. Here we introduce KiloSort, a new integrated spike sorting framework that uses template matching both during spike detection and during spike clustering. KiloSort models the electrical voltage as a sum of template waveforms triggered on the spike times, which allows overlapping spikes to be identified and resolved. Unlike previous algorithms that compress the data with PCA, KiloSort operates on the raw data which allows it to construct a more accurate model of the waveforms. Processing times are faster than in previous algorithms thanks to batch-based optimization on GPUs. We compare KiloSort to an established algorithm and show favorable performance, at much reduced processing times. A novel post-clustering merging step based on the continuity of the templates further reduced substantially the number of manual operations required on this data, for the neurons with near-zero error rates, paving the way for fully automated spike sorting of multichannel electrode recordings.