mtybilly/Instruct2DS huggingface dataset:
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Authors: jean barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, Lenka Zdeborová
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available.
Large Margin Discriminant Dimensionality Reduction in Prediction Space
Authors: Mohammad Saberian, Jose Costa Pereira, Can Xu, Jian Yang, Nuno Nvasconcelos
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: In this paper we establish a duality between boosting and SVM, and use this to derive a novel discriminant dimensionality reduction algorithm. In particular, using the multiclass formulation of boosting and SVM we note that both use a combination of mapping and linear classification to maximize the multiclass margin. In SVM this is implemented using a pre-defined mapping (induced by the kernel) and optimizing the linear classifiers. In boosting the linear classifiers are pre-defined and the mapping (predictor) is learned through combination of weak learners. We argue that the intermediate mapping, e.g. boosting predictor, is preserving the discriminant aspects of the data and by controlling the dimension of this mapping it is possible to achieve discriminant low dimensional representations for the data. We use the aforementioned duality and propose a new method, Large Margin Discriminant Dimensionality Reduction (LADDER) that jointly learns the mapping and the linear classifiers in an efficient manner. This leads to a data-driven mapping which can embed data into any number of dimensions. Experimental results show that this embedding can significantly improve performance on tasks such as hashing and image/scene classification.
Fast learning rates with heavy-tailed losses
Authors: Vu C Dinh, Lam S Ho, Binh Nguyen, Duy Nguyen
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i)  the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ f|$, where $\ell$ is the loss function and $\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\ell$ satisfies the multi-scale Bernstein's condition on $\mathcal{F}$. Under these assumptions, we prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's powers, can be arbitrarily close to $O(n^{-1})$. We then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.
Dynamic matrix recovery from incomplete observations under an exact low-rank constraint
Authors: Liangbei Xu, Mark Davenport
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few.  In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the {\em matrix sensing} and {\em matrix completion} observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.
Tight Complexity Bounds for Optimizing Composite Objectives
Authors: Blake E Woodworth, Nati Srebro
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient descent (AGD) and an accelerated variant of SVRG are optimal in the deterministic and randomized settings respectively, and that a gradient oracle is sufficient for the optimal rate. For non-smooth functions, having access to prox oracles reduces the complexity and we present optimal methods based on smoothing that improve over methods using just gradient accesses.
A forward model at Purkinje cell synapses facilitates cerebellar anticipatory control
Authors: Ivan Herreros, Xerxes Arsiwalla, Paul Verschure
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: How does our motor system solve the problem of anticipatory control in spite of a wide spectrum of response dynamics from different musculo-skeletal systems, transport delays as well as response latencies throughout the central nervous system? To a great extent, our highly-skilled motor responses are a result of a reactive feedback system, originating in the brain-stem and spinal cord, combined with a feed-forward anticipatory system, that is adaptively fine-tuned by sensory experience and originates in the cerebellum. Based on that interaction we design the counterfactual predictive control (CFPC) architecture, an anticipatory adaptive motor control scheme in which a feed-forward module, based on the cerebellum, steers an error feedback controller with counterfactual error signals. Those are signals that trigger reactions as actual errors would, but that do not code for any current of forthcoming errors. In order to determine the optimal learning strategy, we derive a novel learning rule for the feed-forward module that involves an eligibility trace and operates at the synaptic level. In particular, our eligibility trace provides a mechanism beyond co-incidence detection in that it convolves a history of prior synaptic inputs with error signals. In the context of cerebellar physiology, this solution implies that Purkinje cell synapses should generate eligibility traces using a forward model of the system being controlled. From an engineering perspective, CFPC provides a general-purpose anticipatory control architecture equipped with a learning rule that exploits the full dynamics of the closed-loop system.
SURGE: Surface Regularized Geometry Estimation from a Single Image
Authors: Peng Wang, Xiaohui Shen, Bryan Russell, Scott Cohen, Brian Price, Alan L. Yuille
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: This paper introduces an approach to regularize 2.5D surface normal and depth predictions at each pixel given a single input image. The approach infers and reasons about the underlying 3D planar surfaces depicted in the image to snap predicted normals and depths to inferred planar surfaces, all while maintaining fine detail within objects. Our approach comprises two components: (i) a fourstream convolutional neural network (CNN) where depths, surface normals, and likelihoods of planar region and planar boundary are predicted at each pixel, followed by (ii) a dense conditional random field (DCRF) that integrates the four predictions such that the normals and depths are compatible with each other and regularized by the planar region and planar boundary information. The DCRF is formulated such that gradients can be passed to the surface normal and depth CNNs via backpropagation. In addition, we propose new planar wise metrics to evaluate geometry consistency within planar surfaces, which are more tightly related to dependent 3D editing applications. We show that our regularization yields a 30% relative improvement in planar consistency on the NYU v2 dataset.
CliqueCNN: Deep Unsupervised Exemplar Learning
Authors: Miguel A Bautista, Artsiom Sanakoyeu, Ekaterina Tikhoncheva, Bjorn Ommer
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Exemplar learning is a powerful paradigm for discovering visual similarities in an unsupervised manner. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With only a single positive sample, a great imbalance between one positive and many negatives, and unreliable relationships between most samples, training of convolutional neural networks is impaired. Given weak estimates of local distance we propose a single optimization problem to extract batches of samples with mutually consistent relations. Conflicting relations are distributed over different batches and similar samples are grouped into compact cliques. Learning exemplar similarities is framed as a sequence of clique categorization tasks. The CNN then consolidates transitivity relations within and between cliques and learns a single representation for all samples without the need for labels. The proposed unsupervised approach has shown competitive performance on detailed posture analysis and object classification.
Computing and maximizing influence in linear threshold and triggering models
Authors: Justin T Khim, Varun Jog, Po-Ling Loh
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a (1 - 1/e)-factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently. This leads to an attractive, highly scalable algorithm for influence maximization with rigorous theoretical guarantees.
Data Programming: Creating Large Training Sets, Quickly
Authors: Alexander J Ratner, Christopher M De Sa, Sen Wu, Daniel Selsam, Christopher Ré
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Large labeled training sets are the critical building blocks of supervised learning methods and are key enablers of deep learning techniques. For some applications, creating labeled training sets is the most time-consuming and expensive part of applying machine learning. We therefore propose a paradigm for the programmatic creation of training sets called data programming in which users provide a set of labeling functions, which are programs that heuristically label subsets of the data, but that are noisy and may conflict. By viewing these labeling functions as implicitly describing a generative model for this noise, we show that we can recover the parameters of this model to "denoise" the generated training set, and establish theoretically that we can recover the parameters of these generative models in a handful of settings. We then show how to modify a discriminative loss function to make it noise-aware, and demonstrate our method over a range of discriminative models including logistic regression and LSTMs. Experimentally, on the 2014 TAC-KBP Slot Filling challenge, we show that data programming would have led to a new winning score, and also show that applying data programming to an LSTM model leads to a TAC-KBP score almost 6 F1 points over a state-of-the-art LSTM baseline (and into second place in the competition). Additionally, in initial user studies we observed that data programming may be an easier way for non-experts to create machine learning models when training data is limited or unavailable.
Flexible Models for Microclustering with Application to Entity Resolution
Authors: Brenda Betancourt, Giacomo Zanella, Jeffrey W Miller, Hanna Wallach, Abbas Zaidi, Rebecca C. Steorts
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.
Blind Regression: Nonparametric Regression for Latent Variable Models via Collaborative Filtering
Authors: Dogyoon Song, Christina E. Lee, Yihua Li, Devavrat Shah
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We introduce the framework of {\em blind regression} motivated by {\em matrix completion} for recommendation systems: given $m$ users, $n$ movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of non-parametric statistics, we posit that user $u$ and movie $i$ have features $x_1(u)$ and $x_2(i)$ respectively, and their corresponding rating $y(u,i)$ is a noisy measurement of $f(x_1(u), x_2(i))$ for some unknown function $f$. In contrast with classical regression, the features $x = (x_1(u), x_2(i))$ are not observed, making it challenging to apply standard regression methods to  predict the unobserved ratings.  Inspired by the classical Taylor's expansion for differentiable functions, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis through our framework naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering in practice. Assuming each entry is sampled independently with probability at least $\max(m^{-1+\delta},n^{-1/2+\delta})$ with $\delta > 0$, we prove that the expected fraction of our estimates with error greater than $\epsilon$ is less than $\gamma^2 / \epsilon^2$ plus a polynomially decaying term, where $\gamma^2$ is the variance of the additive entry-wise noise term.  Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods.
An ensemble diversity approach to supervised binary hashing
Authors: Miguel A. Carreira-Perpinan, Ramin Raziperchikolaei
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves state-of-the-art precision and recall in experiments with image retrieval.
Learning Influence Functions from Incomplete Observations
Authors: Xinran He, Ke Xu, David Kempe, Yan Liu
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade (DIC) models is established by reducing incomplete observations to complete observations in a modified graph. Our improper PAC learnability result applies for the DLT and DIC models as well as the Continuous-Time Independent Cascade (CIC) model.  It is based on a parametrization in terms of reachability features, and also gives rise to an efficient and practical heuristic. Experiments on synthetic and real-world datasets demonstrate the ability of our method to compensate even for a fairly large fraction of missing observations.
Backprop KF: Learning Discriminative Deterministic State Estimators
Authors: Tuomas Haarnoja, Anurag Ajay, Sergey Levine, Pieter Abbeel
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.
On the Recursive Teaching Dimension of VC Classes
Authors: Xi Chen, Xi Chen, Yu Cheng, Bo Tang
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: The recursive teaching dimension (RTD) of a concept class $C \subseteq \{0, 1\}^n$, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of $C$ in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension.  Given a concept class $C \subseteq \{0, 1\}^n$ with $VCD(C) = d$, we first show that $RTD(C)$ is at most $d 2^{d+1}$. This is the first upper bound for $RTD(C)$ that depends only on $VCD(C)$, independent of the size of the concept class $|C|$ and its~domain size $n$. Before our work, the best known upper bound for $RTD(C)$ is $O(d 2^d \log \log |C|)$, obtained by Moran et al. [MSWY15]. We remove the $\log \log |C|$ factor.  We also improve the lower bound on the worst-case ratio of $RTD(C)$ to $VCD(C)$. We present a family of classes $\{ C_k \}_{k \ge 1}$ with $VCD(C_k) = 3k$ and $RTD(C_k)=5k$, which implies that the ratio of $RTD(C)$ to $VCD(C)$ in the worst case can be as large as $5/3$. Before our work, the largest ratio known was $3/2$ as obtained by Kuhlmann [Kuh99]. Since then, no finite concept class $C$ has been known to satisfy $RTD(C) > (3/2) VCD(C)$.
Generalized Correspondence-LDA Models (GC-LDA) for Identifying Functional Regions in the Brain
Authors: Timothy Rubin, Oluwasanmi O Koyejo, Michael N. Jones, Tal Yarkoni
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.
Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation
Authors: George Papamakarios, Iain Murray
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an ε-ball around the observed data, which is only correct in the limit ε→0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as ε→0, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian conditional density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.
Ladder Variational Autoencoders
Authors: Casper Kaae Sønderby, Tapani Raiko, Lars Maaløe, Søren Kaae Sønderby, Ole Winther
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.
Learning Sparse Gaussian Graphical Models with Overlapping Blocks
Authors: Mohammad Javad Hosseini, Su-In Lee
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We present a novel framework, called GRAB (GRaphical models with overlApping Blocks), to capture densely connected components in a network estimate. GRAB takes as input a data matrix of p variables and n samples, and jointly learns both a network among p variables and densely connected groups of variables (called `blocks'). GRAB has four major novelties as compared to existing network estimation methods: 1) It does not require the blocks to be given a priori. 2) Blocks can overlap. 3) It can jointly learn a network structure and overlapping blocks. 4) It solves a joint optimization problem with the block coordinate descent method that is convex in each step. We show that GRAB reveals the underlying network structure substantially better than four state-of-the-art competitors on synthetic data. When applied to cancer gene expression data, GRAB outperforms its competitors in revealing known functional gene sets and potentially novel genes that drive cancer.
Probabilistic Inference with Generating Functions for Poisson Latent Variable Models
Authors: Kevin Winner, Daniel R. Sheldon
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Graphical models with latent count variables arise in a number of fields. Standard exact inference techniques such as variable elimination and belief propagation do not apply to these models because the latent variables have countably infinite support. As a result, approximations such as truncation or MCMC are employed. We present the first exact inference algorithms for a class of models with latent count variables by developing a novel representation of countably infinite factors as probability generating functions, and then performing variable elimination with generating functions. Our approach is exact, runs in pseudo-polynomial time, and is much faster than existing approximate techniques. It leads to better parameter estimates for problems in population ecology by avoiding error introduced by approximate likelihood computations.
Achieving the KS threshold in the general stochastic block model with linearized acyclic belief propagation
Authors: Emmanuel Abbe, Colin Sandon
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: The stochastic block model (SBM) has long been studied in machine learning and network science as a canonical model for clustering and community detection. In the recent years, new developments have demonstrated the presence of threshold phenomena for this model, which have set new challenges for algorithms. For the {\it detection} problem in symmetric SBMs, Decelle et al.\ conjectured that the so-called Kesten-Stigum (KS) threshold can be achieved efficiently. This was proved for two communities, but remained open from three communities. We prove this conjecture here, obtaining a more general result that applies to arbitrary SBMs with linear size communities. The developed algorithm is a linearized acyclic belief propagation (ABP) algorithm, which mitigates the effects of cycles while provably achieving the KS threshold in $O(n \ln n)$ time. This extends prior methods by achieving universally the KS threshold while reducing or preserving the computational complexity. ABP is also connected to a power iteration method on a generalized nonbacktracking operator, formalizing the spectral-message passing interplay described in Krzakala et al., and extending results from Bordenave et al.
A Unified Approach for Learning the Parameters of Sum-Product Networks
Authors: Han Zhao, Pascal Poupart, Geoffrey J. Gordon
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.
The Multiscale Laplacian Graph Kernel
Authors: Risi Kondor, Horace Pan
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we define in this paper can account for structure at a range of different scales. At the heart of the MLG construction is another new graph kernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has the property that it can lift a base kernel defined on the vertices of two graphs to a kernel between the graphs. The MLG kernel applies such FLG kernels to subgraphs recursively. To make the MLG kernel computationally feasible, we also introduce a randomized projection procedure, similar to the Nystro ̈m method, but for RKHS operators.
Learning the Number of Neurons in Deep Networks
Authors: Jose M Alvarez, Mathieu Salzmann
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them impractical for constrained platforms. These networks, however, are known to have many redundant parameters, and could thus, in principle, be replaced by more compact architectures. In this paper, we introduce an approach to automatically determining the number of neurons in each layer of a deep network during learning. To this end, we propose to make use of a group sparsity regularizer on the parameters of the network, where each group is defined to act on a single neuron. Starting from an overcomplete network, we show that our approach can reduce the number of parameters by up to 80\% while retaining or even improving the network accuracy.
Deep Alternative Neural Network: Exploring Contexts as Early as Possible for Action Recognition
Authors: Jinzhuo Wang, Wenmin Wang, xiongtao Chen, Ronggang Wang, Wen Gao
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Contexts are crucial for action recognition in video. Current methods often mine contexts after extracting hierarchical local features and focus on their high-order encodings. This paper instead explores contexts as early as possible and leverages their evolutions for action recognition. In particular, we introduce a novel architecture called deep alternative neural network (DANN) stacking alternative layers. Each alternative layer consists of a volumetric convolutional layer followed by a recurrent layer. The former acts as local feature learner while the latter is used to collect contexts. Compared with feed-forward neural networks, DANN learns contexts of local features from the very beginning. This setting helps to preserve hierarchical context evolutions which we show are essential to recognize similar actions. Besides, we present an adaptive method to determine the temporal size for network input based on optical flow energy, and develop a volumetric pyramid pooling layer to deal with input clips of arbitrary sizes. We demonstrate the advantages of DANN on two benchmarks HMDB51 and UCF101 and report competitive or superior results to the state-of-the-art.
Online ICA: Understanding Global Dynamics of Nonconvex Optimization via Diffusion Processes
Authors: Chris Junchi Li, Zhaoran Wang, Han Liu
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm based on diffusion processes to characterize the global dynamics of nonconvex statistical optimization. As a concrete example, we study stochastic gradient descent (SGD) for the tensor decomposition formulation of independent component analysis. In particular, we cast different phases of SGD into diffusion processes, i.e., solutions to stochastic differential equations. Initialized from an unstable equilibrium, the global dynamics of SGD transit over three consecutive phases: (i) an unstable Ornstein-Uhlenbeck process slowly departing from the initialization, (ii) the solution to an ordinary differential equation, which quickly evolves towards the desirable local minimum, and (iii) a stable Ornstein-Uhlenbeck process oscillating around the desirable local minimum. Our proof techniques are based upon Stroock and Varadhan’s weak convergence of Markov chains to diffusion processes, which are of independent interest.
Spatio-Temporal Hilbert Maps for Continuous Occupancy Representation in Dynamic Environments
Authors: Ransalu Senanayake, Lionel Ott, Simon O'Callaghan, Fabio T Ramos
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We consider the problem of building continuous occupancy representations in  dynamic environments for robotics applications. The problem has hardly been discussed previously due to the complexity of patterns in urban environments,  which have both spatial and temporal dependencies. We address the problem  as learning a kernel classifier on an efficient feature space. The key novelty of  our approach is the incorporation of variations in the time domain into the spatial  domain. We propose a method to propagate motion uncertainty into the kernel using a hierarchical model. The main benefit of this approach is that it can directly predict  the occupancy state of the map in the future from past observations, being a valuable  tool for robot trajectory planning under uncertainty. Our approach preserves the  main computational benefits of static Hilbert maps — using stochastic gradient  descent for fast optimization of model parameters and incremental updates as  new data are captured. Experiments conducted in road intersections of an urban  environment demonstrated that spatio-temporal Hilbert maps can accurately model  changes in the map while outperforming other techniques on various aspects.
CRF-CNN: Modeling Structured Information in Human Pose Estimation
Authors: Xiao Chu, Wanli Ouyang, hongsheng Li, Xiaogang Wang
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Deep convolutional neural networks (CNN) have achieved great success. On the other hand, modeling structural information has been proved critical in many vision problems. It is of great interest to integrate them effectively. In a classical neural network, there is no message passing between neurons in the same layer. In this paper, we propose a CRF-CNN framework which can simultaneously model structural information in both output and hidden feature layers in a probabilistic way, and it is applied to human pose estimation. A message passing scheme is proposed, so that in various layers each body joint receives messages from all the others in an efficient way. Such message passing can be implemented with convolution between features maps in the same layer, and it is also integrated with feedforward propagation in neural networks. Finally, a neural network implementation of end-to-end learning CRF-CNN is provided. Its effectiveness is demonstrated through experiments on two benchmark datasets.
Bayesian latent structure discovery from multi-neuron recordings
Authors: Scott Linderman, Ryan P. Adams, Jonathan W Pillow
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains.  We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.
Latent Attention For If-Then Program Synthesis
Authors: Chang Liu, Xinyun Chen, Eui Chul Shin, Mingcheng Chen, Dawn Song
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Automatic translation from natural language descriptions into programs is a long-standing challenging problem. In this work, we consider a simple yet important sub-problem: translation from textual  descriptions to If-Then programs. We devise a novel neural network architecture for this task which we train end-to-end. Specifically, we introduce Latent Attention, which computes multiplicative weights for the words in the description in a two-stage process with the goal of better leveraging the natural language structures that indicate the relevant parts for predicting program elements. Our architecture reduces the error rate by 28.57% compared to prior art. We also propose a one-shot learning scenario of If-Then program synthesis and simulate it with our existing dataset. We demonstrate a variation on the training procedure for this scenario that outperforms the original procedure, significantly closing the gap to the model trained with all data.
Understanding Probabilistic Sparse Gaussian Process Approximations
Authors: Matthias Bauer, Mark van der Wilk, Carl Edward Rasmussen
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Good sparse approximations are essential for practical inference in Gaussian Processes as the computational cost of exact methods is prohibitive for large datasets. The Fully Independent Training Conditional (FITC) and the Variational Free Energy (VFE) approximations are two recent popular methods. Despite superficial similarities, these approximations have surprisingly different theoretical properties and behave differently in practice. We thoroughly investigate the two methods for regression both analytically and through illustrative examples, and draw conclusions to guide practical application.
Wasserstein Training of Restricted Boltzmann Machines
Authors: Grégoire Montavon, Klaus-Robert Müller, Marco Cuturi
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale real-world data distributions. Parameters of the model are usually learned by minimizing the Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in this work a novel approach for Boltzmann machine training which assumes that a meaningful metric between observations is known. This metric between observations can then be used to define the Wasserstein distance between the distribution induced by the Boltzmann machine on the one hand, and that given by the training sample on the other hand. We derive a gradient of that distance with respect to the model parameters. Minimization of this new objective leads to generative models with different statistical properties. We demonstrate their practical potential on data completion and denoising, for which the metric between observations plays a crucial role.
A primal-dual method for conic constrained distributed optimization problems
Authors: Necdet Serhat Aybat, Erfan Yazdandoost Hamedani
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We consider cooperative multi-agent consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. We provide convergence rates in sub-optimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithms; and show how to extend these methods to handle time-varying communication networks.
Path-Normalized Optimization of Recurrent Neural Networks with ReLU Activations
Authors: Behnam Neyshabur, Yuhuai Wu, Ruslan Salakhutdinov, Nati Srebro
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: We investigate the parameter-space geometry of recurrent neural networks (RNNs), and develop an adaptation of path-SGD optimization method, attuned to this geometry, that can learn plain RNNs with ReLU activations. On several datasets that require capturing long-term dependency structure, we show that path-SGD can significantly improve trainability of ReLU RNNs compared to RNNs trained with SGD, even with various recently suggested initialization schemes.
Communication-Optimal Distributed Clustering
Authors: Jiecao Chen, He Sun, David Woodruff, Qin Zhang
Published in: Advances in Neural Information Processing Systems 29  (NIPS 2016) (Main Conference Track), 2016

Abstract: Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would like the quality of the clustering in the distributed setting to match that in the centralized setting for which all the data resides on a single site. In this work, we study both graph and geometric clustering problems in two distributed models: (1) a point-to-point model, and (2) a model with a broadcast channel. We give protocols in both models which we show are nearly optimal by proving almost matching communication lower bounds. Our work highlights the surprising power of a broadcast channel for clustering problems; roughly speaking, to cluster n points or n vertices in a graph distributed across s servers, for a worst-case partitioning the communication complexity in a point-to-point model is n*s, while in the broadcast model it is n + s. We implement our algorithms and demonstrate this phenomenon on real life datasets, showing that our algorithms are also very efficient in practice.