mtybilly/Instruct2DS huggingface dataset:
LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
Authors: CHRISTOS THRAMPOULIDIS, Ehsan Abbasi, Babak Hassibi
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Consider estimating an unknown, but structured (e.g. sparse, low-rank, etc.), signal $x_0\in R^n$ from a vector $y\in R^m$ of measurements of the form $y_i=g_i(a_i^Tx_0)$, where the $a_i$'s are the rows of a known measurement matrix $A$, and, $g$ is a (potentially unknown) nonlinear and random link-function. Such measurement functions could arise in applications where the measurement device has nonlinearities and uncertainties. It could also arise by design, e.g., $g_i(x)=sign(x+z_i)$, corresponds to noisy 1-bit quantized measurements. Motivated by the classical work of Brillinger, and more recent work of Plan and Vershynin, we estimate $x_0$ via solving the Generalized-LASSO, i.e., $\hat x=\arg\min_{x}\|y-Ax_0\|_2+\lambda f(x)$ for some regularization parameter $\lambda >0$ and some (typically non-smooth) convex regularizer $f$ that promotes the structure of $x_0$, e.g. $\ell_1$-norm, nuclear-norm. While this approach seems to naively ignore the nonlinear function $g$, both Brillinger and Plan and Vershynin have shown that, when the entries of $A$ are iid standard normal, this is a good estimator of $x_0$ up to a constant of proportionality $\mu$, which only depends on $g$. In this work, we considerably strengthen these results by obtaining explicit expressions for $\|\hat x-\mu x_0\|_2$, for the regularized Generalized-LASSO, that are asymptotically precise when $m$ and $n$ grow large. A main result is that the estimation performance of the Generalized LASSO with non-linear measurements is asymptotically the same as one whose measurements are linear $y_i=\mu a_i^Tx_0+\sigma z_i$, with $\mu=E[\gamma g(\gamma)]$ and $\sigma^2=E[(g(\gamma)-\mu\gamma)^2]$, and, $\gamma$ standard normal. The derived expressions on the estimation performance are the first-known precise results in this context. One interesting consequence of our result is that the optimal quantizer of the measurements that minimizes the estimation error of the LASSO is the celebrated Lloyd-Max quantizer.
Natural Neural Networks
Authors: Guillaume Desjardins, Karen Simonyan, Razvan Pascanu, koray kavukcuoglu
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We introduce Natural Neural Networks, a novel family of algorithms that speed up convergence by adapting their internal representation during training to improve conditioning of the Fisher matrix. In particular, we show a specific example that employs a simple and efficient reparametrization of the neural network weights by implicitly whitening the representation obtained at each layer, while preserving the feed-forward computation of the network. Such networks can be trained efficiently via the proposed Projected Natural Gradient Descent algorithm (PRONG), which amortizes the cost of these reparametrizations over many parameter updates and is closely related to the Mirror Descent online learning algorithm. We highlight the benefits of our method on both unsupervised and supervised learning tasks, and showcase its scalability by training on the large-scale ImageNet Challenge dataset.
Scalable Adaptation of State Complexity for Nonparametric Hidden Markov Models
Authors: Michael C Hughes, William T Stephenson, Erik Sudderth
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Bayesian nonparametric hidden Markov models are typically learned via fixed truncations of the infinite state space or local Monte Carlo proposals that make small changes to the state space. We develop an inference algorithm for the sticky hierarchical Dirichlet process hidden Markov model that scales to big datasets by processing a few sequences at a time yet allows rapid adaptation of the state space cardinality. Unlike previous point-estimate methods, our novel variational bound penalizes redundant or irrelevant states and thus enables optimization of the state space. Our birth proposals use observed data statistics to create useful new states that escape local optima. Merge and delete proposals remove ineffective states to yield simpler models with more affordable future computations. Experiments on speaker diarization, motion capture, and epigenetic chromatin datasets discover models that are more compact, more interpretable, and better aligned to ground truth segmentations than competitors. We have released an open-source Python implementation which can parallelize local inference steps across sequences.
Inference for determinantal point processes without spectral knowledge
Authors: Rémi Bardenet, Michalis Titsias RC AUEB
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Determinantal point processes (DPPs) are point process models thatnaturally encode diversity between the points of agiven realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exactsampling or analyticity of the moments, but learning the parameters ofkernel $K$ through likelihood-based inference is notstraightforward. First, the kernel that appears in thelikelihood is not $K$, but another kernel $L$ related to $K$ throughan often intractable spectral decomposition. This issue is typically bypassed in machine learning bydirectly parametrizing the kernel $L$, at the price of someinterpretability of the model parameters. We follow this approachhere. Second, the likelihood has an intractable normalizingconstant, which takes the form of large determinant in the case of aDPP over a finite set of objects, and the form of a Fredholm determinant in thecase of a DPP over a continuous domain. Our main contribution is to derive bounds on the likelihood ofa DPP, both for finite and continuous domains. Unlike previous work, our bounds arecheap to evaluate since they do not rely on approximating the spectrumof a large matrix or an operator. Through usual arguments, these bounds thus yield cheap variationalinference and moderately expensive exact Markov chain Monte Carlo inference methods for DPPs.
A Bayesian Framework for Modeling Confidence in Perceptual Decision Making
Authors: Koosha Khalvati, Rajesh P. Rao
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: The degree of confidence in one's choice or decision is a critical aspect of perceptual decision making. Attempts to quantify a decision maker's confidence by measuring accuracy in a task have yielded limited success because confidence and accuracy are typically not equal. In this paper, we introduce a Bayesian framework to model confidence in perceptual decision making. We show that this model, based on partially observable Markov decision processes (POMDPs), is able to predict confidence of a decision maker based only on the data available to the experimenter. We test our model on two experiments on confidence-based decision making involving the well-known random dots motion discrimination task. In both experiments, we show that our model's predictions closely match experimental data. Additionally, our model is also consistent with other phenomena such as the hard-easy effect in perceptual decision making.
Sample Complexity of Episodic Fixed-Horizon Reinforcement Learning
Authors: Christoph Dann, Emma Brunskill
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds.  However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of episodes required to guarantee a certain performance with high probability (PAC guarantee). In this paper, we derive an upper PAC bound of order O(|S|²|A|H² log(1/δ)/ɛ²)  and a lower PAC bound Ω(|S||A|H² log(1/(δ+c))/ɛ²) (ignoring log-terms) that match up to log-terms and an additional linear dependency on the number of states |S|.  The lower bound is the first of its kind for this setting. Our upper bound leverages Bernstein's inequality to improve on previous bounds for episodic finite-horizon MDPs which have a time-horizon dependency of at least H³.
Algorithms with Logarithmic or Sublinear Regret for  Constrained Contextual Bandits
Authors: Huasen Wu, R. Srikant, Xin Liu, Chong Jiang
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We study contextual bandits with budget and time constraints under discrete contexts, referred to as constrained contextual bandits. The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming(ALP), which achieves near-optimality and only requires the ordering of expected rewards. With these highly desirable features,  we  then combine ALP with the upper-confidence-bound (UCB) method in the general case where the expected rewards are unknown a priori. We show that the proposed UCB-ALP algorithm achieves logarithmic regret except in certain boundary cases.Further, we design algorithms and obtain similar regret analysis results for  more general systems with unknown context distribution or heterogeneous costs.  To the best of our knowledge, this is the  first work that shows how to achieve logarithmic regret in constrained contextual bandits. Moreover, this work also sheds light on the study of computationally efficient algorithms for general constrained contextual bandits.
Latent Bayesian melding for integrating individual and population models
Authors: Mingjun Zhong, Nigel Goddard, Charles Sutton
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour,  whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matchingexpectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.
Regressive Virtual Metric Learning
Authors: Michaël Perrot, Amaury Habrard
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We are interested in supervised metric learning of Mahalanobis like distances. Existing approaches mainly focus on learning a new distance using similarity and dissimilarity constraints between examples. In this paper, instead of bringing closer examples of the same class and pushing far away examples of different classes we propose to move the examples with respect to virtual points. Hence, each example is brought closer to a a priori defined virtual point reducing the number of constraints to satisfy. We show that our approach admits a closed form solution which can be kernelized. We provide a theoretical analysis showing the consistency of the approach and establishing some links with other classical metric learning methods. Furthermore we propose an efficient solution to the difficult problem of selecting virtual points based in part on recent works in optimal transport. Lastly, we evaluate our approach on several state of the art datasets.
Halting in Random Walk Kernels
Authors: Mahito Sugiyama, Karsten Borgwardt
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Random walk kernels measure graph similarity by counting matching walks in two graphs. In their most popular form of geometric random walk kernels, longer walks of length $k$ are downweighted by a factor of $\lambda^k$ ($\lambda < 1$) to ensure convergence of the corresponding geometric series. We know from the field of link prediction that this downweighting often leads to a phenomenon referred to as halting: Longer walks are downweighted so much that the similarity score is completely dominated by the comparison of walks of length 1. This is a naive kernel between edges and vertices. We theoretically show that halting may occur in geometric random walk kernels. We also empirically quantify its impact in simulated datasets and popular graph classification benchmark datasets. Our findings promise to be instrumental in future graph kernel development and applications of random walk kernels.
Kullback-Leibler Proximal Variational Inference
Authors: Mohammad Emtiyaz Khan, Pierre Baque, François Fleuret, Pascal Fua
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We propose a new variational inference method based on the Kullback-Leibler (KL) proximal term. We make two contributions towards improving efficiency of variational inference. Firstly, we derive a KL proximal-point algorithm and show its equivalence to gradient descent with natural gradient in stochastic variational inference. Secondly, we use the proximal framework to derive efficient variational algorithms for non-conjugate models. We propose a splitting procedure to separate non-conjugate terms from conjugate ones. We then linearize the non-conjugate terms and show that the resulting subproblem admits a closed-form solution. Overall, our approach converts a non-conjugate model to subproblems that involve inference in well-known conjugate models. We apply our method to many models and derive generalizations for non-conjugate exponential family. Applications to real-world datasets show that our proposed algorithms are easy to implement, fast to converge, perform well, and reduce computations.
A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements
Authors: Qinqing Zheng, John Lafferty
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs.  With $O(r^3 \kappa^2 n \log n)$ random measurements of a positive semidefinite $n\times n$ matrix of rank $r$ and condition number $\kappa$, our method is guaranteed to converge linearly to the global optimum.
On-the-Job Learning with Bayesian Decision Theory
Authors: Keenon Werling, Arun Tejasvi Chaganty, Percy Liang, Christopher D. Manning
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Our goal is to deploy a high-accuracy system starting with zero training examples. We consider an “on-the-job” setting, where as inputs arrive, we use real-time crowdsourcing to resolve uncertainty where needed and output our prediction when confident. As the model improves over time, the reliance on crowdsourcing queries decreases. We cast our setting as a stochastic game based on Bayesian decision theory, which allows us to balance latency, cost, and accuracy objectives in a principled way. Computing the optimal policy is intractable, so we develop an approximation based on Monte Carlo Tree Search. We tested our approach on three datasets-- named-entity recognition, sentiment classification, and image classification. On the NER task we obtained more than an order of magnitude reduction in cost compared to full human annotation, while boosting performance relative to the expert provided labels. We also achieve a 8% F1 improvement over having a single human label the whole set, and a 28% F1 improvement over online learning.
Spatial Transformer Networks
Authors: Max Jaderberg, Karen Simonyan, Andrew Zisserman, koray kavukcuoglu
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Convolutional Neural Networks define an exceptionallypowerful class of model, but are still limited by the lack of abilityto be spatially invariant to the input data in a computationally and parameterefficient manner. In this work we introduce a new learnable module, theSpatial Transformer, which explicitly allows the spatial manipulation ofdata within the network. This differentiable module can be insertedinto existing convolutional architectures, giving neural networks the ability toactively spatially transform feature maps, conditional on the feature map itself,without any extra training supervision or modification to the optimisation process. We show that the useof spatial transformers results in models which learn invariance to translation,scale, rotation and more generic warping, resulting in state-of-the-artperformance on several benchmarks, and for a numberof classes of transformations.
Precision-Recall-Gain Curves: PR Analysis Done Right
Authors: Peter Flach, Meelis Kull
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Precision-Recall analysis abounds in applications of binary classification where true negatives do not add value and hence should not affect assessment of the classifier's performance. Perhaps inspired by the many advantages of receiver operating characteristic (ROC) curves and the area under such curves for accuracy-based performance assessment, many researchers have taken to report Precision-Recall (PR) curves and associated areas as performance metric. We demonstrate in this paper that this practice is fraught with difficulties, mainly because of incoherent scale assumptions -- e.g., the area under a PR curve takes the arithmetic mean of precision values whereas the $F_{\beta}$ score applies the harmonic mean. We show how to fix this by plotting PR curves in a different coordinate system, and demonstrate that the new Precision-Recall-Gain curves inherit all key advantages of ROC curves. In particular, the area under Precision-Recall-Gain curves conveys an expected $F_1$ score on a harmonic scale, and the convex hull of a Precision-Recall-Gain curve allows us to calibrate the classifier's scores so as to determine, for each operating point on the convex hull, the interval of $\beta$ values for which the point optimises $F_{\beta}$. We demonstrate experimentally that the area under traditional PR curves can easily favour models with lower expected $F_1$ score than others, and so the use of Precision-Recall-Gain curves will result in better model selection.
Planar Ultrametrics for Image Segmentation
Authors: Julian E Yarkony, Charless Fowlkes
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of finding the closest ultrametric to a specified set of distances and solve it using an LP relaxation that leverages minimum cost perfect matching as a subroutine to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.
Sparse Local Embeddings for Extreme Multi-label Classification
Authors: Kush Bhatia, Himanshu Jain, Purushottam Kar, Manik Varma, Prateek Jain
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and prediction tractable by assuming that the training label matrix is low-rank and hence the effective number of labels can be reduced by projecting the high dimensional label vectors onto a low dimensional linear subspace. Still, leading embedding approaches have been unable to deliver high prediction accuracies or scale to large problems as the low rank assumption is violated in most real world applications.This paper develops the SLEEC classifier to address both limitations. The main technical contribution in SLEEC is a formulation for learning a small ensemble of local distance preserving embeddings which can accurately predict infrequently occurring (tail) labels. This allows SLEEC to break free of the traditional low-rank assumption and boost classification accuracy by learning embeddings which preserve pairwise distances between only the nearest label vectors. We conducted extensive experiments on several real-world as well as benchmark data sets and compare our method against state-of-the-art methods for extreme multi-label classification. Experiments reveal that SLEEC can make significantly more accurate predictions then the state-of-the-art methods including both embeddings (by as much as 35%) as well as trees (by as much as 6%). SLEEC can also scale efficiently to data sets with a million labels which are beyond the pale of leading embedding methods.
Super-Resolution Off the Grid
Authors: Qingqing Huang, Sham M. Kakade
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to biology to spectroscopy, where it is common to take (coarse) Fourier measurements of an object. Of particular interest is in obtaining estimation procedures which are robust to noise, with the following desirable statistical and computational properties: we seek to use coarse Fourier measurements (bounded by some \emph{cutoff frequency}); we hope to take a (quantifiably) small number of measurements; we desire our algorithm to run quickly.  Suppose we have $k$ point sources in $d$ dimensions, where the points are separated by at least $\Delta$ from each other (in Euclidean distance). This work provides an algorithm with the following favorable guarantees:1. The algorithm uses Fourier measurements, whose frequencies are bounded by $O(1/\Delta)$ (up to log factors). Previous algorithms require a \emph{cutoff frequency}  which may be as large as  $\Omega(\sqrt{d}/\Delta)$.2. The number of measurements taken by and the computational complexity of our algorithm are bounded by a polynomial in both the number of points $k$ and the dimension $d$, with \emph{no} dependence on the separation $\Delta$. In contrast, previous algorithms depended inverse polynomially  on the minimal separation and exponentially on the dimension for both of these quantities.Our estimation procedure itself is simple: we take random bandlimited measurements (as opposed to taking an exponential number of measurements on the hyper-grid). Furthermore, our analysis and algorithm are elementary (based on concentration bounds of sampling and singular value decomposition).
Automatic Variational Inference in Stan
Authors: Alp Kucukelbir, Rajesh Ranganath, Andrew Gelman, David Blei
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Variational inference is a scalable technique for approximate Bayesian inference.  Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use.  We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system.  In ADVI the user provides a Bayesian model and a dataset, nothing else.  We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images.  With ADVI we can use variational inference on any model we write in Stan.
Extending Gossip Algorithms to Distributed Estimation of U-statistics
Authors: Igor Colin, Aurélien Bellet, Joseph Salmon, Stéphan Clémençon
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the U-statistic of interest. We establish convergence rate bounds of O(1 / t) and O(log t / t) for the synchronous and asynchronous cases respectively, where t is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.
Model-Based Relative Entropy Stochastic Search
Authors: Abbas Abdolmaleki, Rudolf Lioutikov, Jan R Peters, Nuno Lau, Luis Pualo Reis, Gerhard Neumann
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Stochastic search algorithms are general black-box optimizers. Due to their ease of use and their generality, they have recently also gained a lot of attention in operations research, machine learning and policy search. Yet, these algorithms require a lot of evaluations of the objective, scale poorly with the problem dimension, are affected by highly noisy objective functions and may converge prematurely. To alleviate these problems, we introduce a new surrogate-based stochastic search approach. We learn simple, quadratic surrogate models of the objective function. As the quality of such a quadratic approximation is limited, we do not greedily exploit the learned models. The algorithm can be misled by an inaccurate optimum introduced by the surrogate. Instead, we use information theoretic constraints to bound the `distance' between the new and old data distribution while maximizing the objective function. Additionally the new method is able to sustain the exploration of the search distribution to avoid premature convergence. We compare our method with state of art black-box optimization methods on standard uni-modal and multi-modal optimization functions, on simulated planar robot tasks and a complex robot ball throwing task.The proposed method considerably outperforms the existing approaches.
Semi-supervised Learning with Ladder Networks
Authors: Antti Rasmus, Mathias Berglund, Mikko Honkala, Harri Valpola, Tapani Raiko
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on top of the Ladder network proposed by Valpola (2015) which we extend by combining the model with supervision. We show that the resulting model reaches state-of-the-art performance in semi-supervised MNIST and CIFAR-10 classification in addition to permutation-invariant MNIST classification with all labels.
Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces
Authors: Takashi Takenouchi, Takafumi Kanamori
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality, and reveal a relationship with the alpha-divergence. Small experiments show that the proposed estimator attains comparable performance to the MLE with drastically lower computational cost.
Enforcing balance allows local supervised learning in spiking recurrent networks
Authors: Ralph Bourdoukan, Sophie Denève
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: To predict sensory inputs or control motor trajectories, the brain must constantly learn temporal dynamics based on error feedback. However, it remains unclear how such supervised learning is implemented in biological neural networks. Learning in recurrent spiking networks is notoriously difficult because local changes in connectivity may have an unpredictable effect on the global dynamics. The most commonly used learning rules, such as temporal back-propagation, are not local and thus not biologically plausible. Furthermore, reproducing the Poisson-like statistics of neural responses requires the use of networks with balanced excitation and inhibition. Such balance is easily destroyed during learning. Using a top-down approach, we show how networks of integrate-and-fire neurons can learn arbitrary linear dynamical systems by feeding back their error as a feed-forward input. The network uses two types of recurrent connections: fast and slow. The fast connections learn to balance excitation and inhibition using a voltage-based plasticity rule. The slow connections are trained to minimize the error feedback using a current-based Hebbian learning rule. Importantly, the balance maintained by fast connections is crucial to ensure that global error signals are available locally in each neuron, in turn resulting in a local learning rule for the slow connections. This demonstrates that spiking networks can learn complex dynamics using purely local learning rules, using E/I balance as the key rather than an additional constraint. The resulting network implements a given function within the predictive coding scheme, with minimal dimensions and activity.
Online Learning for Adversaries with Memory: Price of Past Mistakes
Authors: Oren Anava, Elad Hazan, Shie Mannor
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: The framework of online learning with memory naturally captures learning problems with temporal effects, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online Convex Optimization (OCO) framework, and present two algorithms that attain low regret. The first algorithm applies to Lipschitz continuous loss functions, obtaining optimal regret bounds for both convex and strongly convex losses. The second algorithm attains the optimal regret bounds and applies more broadly to convex losses without requiring Lipschitz continuity, yet is more complicated to implement. We complement the theoretic results with two applications: statistical arbitrage in finance, and multi-step ahead prediction in statistics.
Streaming, Distributed Variational Inference for Bayesian Nonparametrics
Authors: Trevor Campbell, Julian Straub, John W. Fisher III, Jonathan P How
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational posterior for each, and make asynchronous streaming updates to a central model. In contrast to previous algorithms, the proposed framework is truly streaming, distributed, asynchronous, learning-rate-free, and truncation-free. The key challenge in developing the framework, arising from fact that BNP models do not impose an inherent ordering on their components, is finding the correspondence between minibatch and central BNP posterior components before performing each update. To address this, the paper develops a combinatorial optimization problem over component correspondences, and provides an efficient solution technique. The paper concludes with an application of the methodology to the DP mixture model, with experimental results demonstrating its practical scalability and performance.
Tree-Guided MCMC Inference for Normalized Random Measure Mixture Models
Authors: Juho Lee, Seungjin Choi
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and their convergence is well studied. However, MCMC often suffers from slow convergence when the acceptance rate is low. Tree-based inference is an alternative deterministic posterior inference method, where Bayesian hierarchical clustering (BHC) or incremental Bayesian hierarchical clustering (IBHC) have been developed for DP or NRM mixture (NRMM) models, respectively. Although IBHC is a promising method for posterior inference for NRMM models due to its efficiency and applicability to online inference, its convergence is not guaranteed since it uses heuristics that simply selects the best solution after multiple trials are made. In this paper, we present a hybrid inference algorithm for NRMM models, which combines the merits of both MCMC and IBHC. Trees built by IBHC outlinespartitions of data, which guides Metropolis-Hastings procedure to employ appropriate proposals. Inheriting the nature of MCMC, our tree-guided MCMC (tgMCMC) is guaranteed to converge, and enjoys the fast convergence thanks to the effective proposals guided by trees. Experiments on both synthetic and real world datasets demonstrate the benefit of our method.
The Self-Normalized Estimator for Counterfactual Learning
Authors: Adith Swaminathan, Thorsten Joachims
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: This paper identifies a severe problem of the counterfactual risk estimator typically used in batch learning from logged bandit feedback (BLBF), and proposes the use of an alternative estimator that avoids this problem.In the BLBF setting, the learner does not receive full-information feedback like in supervised learning, but observes feedback only for the actions taken by a historical policy.This makes BLBF algorithms particularly attractive for training online systems (e.g., ad placement, web search, recommendation) using their historical logs.The Counterfactual Risk Minimization (CRM) principle offers a general recipe for designing BLBF algorithms. It requires a counterfactual risk estimator, and virtually all existing works on BLBF have focused on a particular unbiased estimator.We show that this conventional estimator suffers from apropensity overfitting problem when used for learning over complex hypothesis spaces.We propose to replace the risk estimator with a self-normalized estimator, showing that it neatly avoids this problem.This naturally gives rise to a new learning algorithm -- Normalized Policy Optimizer for Exponential Models (Norm-POEM) --for structured output prediction using linear rules.We evaluate the empirical effectiveness of Norm-POEM on severalmulti-label classification problems, finding that it consistently outperforms the conventional estimator.
Information-theoretic lower bounds for convex optimization with erroneous oracles
Authors: Yaron Singer, Jan Vondrak
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle. In particular, for a given function $x \to f(x)$ we consider optimization when one is given access to absolute error oracles that return values in [f(x) - \epsilon,f(x)+\epsilon] or relative error oracles that return value in [(1+\epsilon)f(x), (1 +\epsilon)f (x)], for some \epsilon larger than 0. We show stark information theoretic impossibility results for minimizing convex functions and maximizing concave functions over polytopes in this model.
A Nonconvex Optimization Framework for Low Rank Matrix Estimation
Authors: Tuo Zhao, Zhaoran Wang, Han Liu
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We study the estimation of low rank matrices via nonconvex optimization. Compared with convex relaxation, nonconvex optimization exhibits superior empirical performance for large scale instances of low rank matrix estimation. However, the understanding of its theoretical guarantees are limited. In this paper, we define the notion of projected oracle divergence based on which we establish sufficient conditions for the success of nonconvex optimization. We illustrate the consequences of this general framework for matrix sensing and completion. In particular, we prove that a broad class of nonconvex optimization algorithms, including alternating minimization and gradient-type methods, geometrically converge to the global optimum and exactly recover the true low rank matrices under standard conditions.
Recursive Training of 2D-3D Convolutional Networks for Neuronal Boundary Prediction
Authors: Kisuk Lee, Aleksandar Zlateski, Vishwanathan Ashwin, H. Sebastian Seung
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Efforts to automate the reconstruction of neural circuits from 3D electron microscopic (EM) brain images are critical for the field of connectomics. An important computation for reconstruction is the detection of neuronal boundaries. Images acquired by serial section EM, a leading 3D EM technique, are highly anisotropic, with inferior quality along the third dimension. For such images, the 2D max-pooling convolutional network has set the standard for performance at boundary detection. Here we achieve a substantial gain in accuracy through three innovations. Following the trend towards deeper networks for object recognition, we use a much deeper network than previously employed for boundary detection. Second, we incorporate 3D as well as 2D filters, to enable computations that use 3D context. Finally, we adopt a recursively trained architecture in which a first network generates a preliminary boundary map that is provided as input along with the original image to a second network that generates a final boundary map. Backpropagation training is accelerated by ZNN, a new implementation of 3D convolutional networks that uses multicore CPU parallelism for speed. Our hybrid 2D-3D architecture could be more generally applicable to other types of anisotropic 3D images, including video, and our recursive framework for any image labeling problem.
Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms
Authors: Yunwen Lei, Urun Dogan, Alexander Binder, Marius Kloft
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially improving the state-of-the-art linear dependence in the existing data-dependent generalization analysis. The theoretical analysis motivates us to introduce a new multi-class classification machine based on lp-norm regularization, where the parameter p controls the complexity of the corresponding bounds. We derive an efficient optimization algorithm based on Fenchel duality theory. Benchmarks on several real-world datasets show that the proposed algorithm can achieve significant accuracy gains over the state of the art.
Scalable Inference for Gaussian Process Models with Black-Box Likelihoods
Authors: Amir Dezfouli, Edwin V. Bonilla
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We propose a sparse method for scalable automated variational inference (AVI) in a large class of models with Gaussian process (GP) priors, multiple latent functions, multiple outputs and non-linear likelihoods. Our approach maintains the statistical efficiency property of the original AVI method, requiring only expectations over univariate Gaussian distributions to approximate the posterior with a mixture of Gaussians. Experiments on small datasets for various problems including  regression, classification, Log Gaussian Cox processes, and warped GPs show that our method can perform as well as the full method under high levels of sparsity. On larger experiments using the MNIST and the SARCOS datasets we show that our method can provide superior performance to previously published scalable approaches that have been handcrafted to specific likelihood models.
M-Best-Diverse Labelings for Submodular Energies and Beyond
Authors: Alexander Kirillov, Dmytro Shlezinger, Dmitry P Vetrov, Carsten Rother, Bogdan Savchynskyy
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: We consider the problem of finding M best diverse solutions of energy minimization problems for graphical models. Contrary to the sequential method of Batra et al., which greedily finds one solution after another, we infer all $M$ solutions jointly. It was shown recently that such jointly inferred labelings not only have smaller total energy but also qualitatively outperform the sequentially obtained ones. The only obstacle for using this new technique is the complexity of the corresponding inference problem, since it is considerably slower algorithm than the method of Batra et al. In this work we show that the joint inference of $M$ best diverse solutions can be formulated as a submodular energy minimization if the original MAP-inference problem is submodular, hence fast inference techniques can be used. In addition to the theoretical results we provide practical algorithms that outperform the current state-of-the art and can be used in both submodular and non-submodular case.
BinaryConnect: Training Deep Neural Networks with binary weights during propagations
Authors: Matthieu Courbariaux, Yoshua Bengio, Jean-Pierre David
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possible values (e.g. -1 or 1), would bring great benefits to specialized DL hardware by replacing many multiply-accumulate operations by simple accumulations, as multipliers are the most space and power-hungry components of the digital implementation of neural networks. We introduce BinaryConnect, a method which consists in training a DNN with binary weights during the forward and backward propagations, while retaining precision of the stored weights in which gradients are accumulated. Like other dropout schemes, we show that BinaryConnect acts as regularizer and we obtain near state-of-the-art results with BinaryConnect on the permutation-invariant MNIST, CIFAR-10 and SVHN.
No-Regret Learning in Bayesian Games
Authors: Jason Hartline, Vasilis Syrgkanis, Eva Tardos
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Recent price-of-anarchy analyses of games of complete information suggest that coarse correlated equilibria, which characterize outcomes resulting from no-regret learning dynamics, have near-optimal welfare. This work provides two main technical results that lift this conclusion to games of incomplete information, a.k.a., Bayesian games. First, near-optimal welfare in Bayesian games follows directly from the smoothness-based proof of near-optimal welfare in the same game when the private information is public.  Second, no-regret learning dynamics converge to Bayesian coarse correlated equilibrium in these incomplete information games. These results are enabled by interpretation of a Bayesian game as a stochastic game of complete information.
Robust Gaussian Graphical Modeling with the Trimmed Graphical Lasso
Authors: Eunho Yang, Aurelie C. Lozano
Published in: Advances in Neural Information Processing Systems 28  (NIPS 2015) (Main Conference Track), 2015

Abstract: Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs.  Our method guards against outliers by an implicit trimming mechanism akin to the popular Least Trimmed Squares method used for linear regression. We provide a rigorous statistical analysis of our estimator in the high-dimensional setting. In contrast, existing approaches for robust sparse GGMs estimation lack statistical guarantees. Our theoretical results are complemented by experiments on simulated and real gene expression data which further demonstrate the value of our approach.