NeurIPS 2016 Papers

We learn rich natural sound representations by capitalizing on large amounts of unlabeled sound data collected in the wild. We leverage the natural synchronization between vision and sound to learn an acoustic representation using two-million unlabeled videos. Unlabeled video has the advantage that it can be economically acquired at massive scales, yet contains useful signals about natural sound. We propose a student-teacher training procedure which transfers discriminative visual knowledge from well established visual recognition models into the sound modality using unlabeled video as a bridge. Our sound representation yields significant performance improvements over the state-of-the-art results on standard benchmarks for acoustic scene/object classification. Visualizations suggest some high-level semantics automatically emerge in the sound network, even though it is trained without ground truth labels.

We study a surprising phenomenon related to the representation of a cloud of data points using polynomials. We start with the previously unnoticed empirical observation that, given a collection (a cloud) of data points, the sublevel sets of a certain distinguished polynomial capture the shape of the cloud very accurately. This distinguished polynomial is a sum-of-squares (SOS) derived in a simple manner from the inverse of the empirical moment matrix. In fact, this SOS polynomial is directly related to orthogonal polynomials and the Christoffel function. This allows to generalize and interpret extremality properties of orthogonal polynomials and to provide a mathematical rationale for the observed phenomenon. Among diverse potential applications, we illustrate the relevance of our results on a network intrusion detection task for which we obtain performances similar to existing dedicated methods reported in the literature.

This paper puts forth a novel algorithm, termed \emph{truncated generalized gradient flow} (TGGF), to solve for $\bm{x}\in\mathbb{R}^n/\mathbb{C}^n$ a system of $m$ quadratic equations $y_i=|\langle\bm{a}_i,\bm{x}\rangle|^2$, $i=1,2,\ldots,m$, which even for $\left\{\bm{a}_i\in\mathbb{R}^n/\mathbb{C}^n\right\}_{i=1}^m$ random is known to be \emph{NP-hard} in general. We prove that as soon as the number of equations $m$ is on the order of the number of unknowns $n$, TGGF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with the time required to read the data $\left\{\left(\bm{a}_i;\,y_i\right)\right\}_{i=1}^m$. Specifically, TGGF proceeds in two stages: s1) A novel \emph{orthogonality-promoting} initialization that is obtained with simple power iterations; and, s2) a refinement of the initial estimate by successive updates of scalable \emph{truncated generalized gradient iterations}. The former is in sharp contrast to the existing spectral initializations, while the latter handles the rather challenging nonconvex and nonsmooth \emph{amplitude-based} cost function. Numerical tests demonstrate that: i) The novel orthogonality-promoting initialization method returns more accurate and robust estimates relative to its spectral counterparts; and ii) even with the same initialization, our refinement/truncation outperforms Wirtinger-based alternatives, all corroborating the superior performance of TGGF over state-of-the-art algorithms.

Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR

This paper studies single-image depth perception in the wild, i.e., recovering depth from a single image taken in unconstrained settings. We introduce a new dataset “Depth in the Wild” consisting of images in the wild annotated with relative depth between pairs of random points. We also propose a new algorithm that learns to estimate metric depth using annotations of relative depth. Compared to the state of the art, our algorithm is simpler and performs better. Experiments show that our algorithm, combined with existing RGB-D data and our new relative depth annotations, significantly improves single-image depth perception in the wild.

In this paper we present a new algorithm for computing a low rank approximation of the product $A^TB$ by taking only a single pass of the two matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch $A$ and $B$ individually, and then (b) find the top components using PCA on the sketch. Our algorithm in contrast retains additional summary information about $A,B$ (e.g. row and column norms etc.) and uses this additional information to obtain an improved approximation from the sketches. Our main analytical result establishes a comparable spectral norm guarantee to existing two-pass methods; in addition we also provide results from an Apache Spark implementation that shows better computational and statistical performance on real-world and synthetic evaluation datasets.

Weighted minwise hashing (WMH) is one of the fundamental subroutine, required by many celebrated approximation algorithms, commonly adopted in industrial practice for large -scale search and learning. The resource bottleneck with WMH is the computation of multiple (typically a few hundreds to thousands) independent hashes of the data. We propose a simple rejection type sampling scheme based on a carefully designed red-green map, where we show that the number of rejected sample has exactly the same distribution as weighted minwise sampling. The running time of our method, for many practical datasets, is an order of magnitude smaller than existing methods. Experimental evaluations, on real datasets, show that for computing 500 WMH, our proposal can be 60000x faster than the Ioffe's method without losing any accuracy. Our method is also around 100x faster than approximate heuristics capitalizing on the efficient ``densified" one permutation hashing schemes~\cite{Proc:OneHashLSH

Faced with saturation of Moore's law and increasing size and dimension of data, system designers have increasingly resorted to parallel and distributed computing to reduce computation time of machine-learning algorithms. However, distributed computing is often bottle necked by a small fraction of slow processors called "stragglers" that reduce the speed of computation because the fusion node has to wait for all processors to complete their processing. To combat the effect of stragglers, recent literature proposes introducing redundancy in computations across processors, e.g., using repetition-based strategies or erasure codes. The fusion node can exploit this redundancy by completing the computation using outputs from only a subset of the processors, ignoring the stragglers. In this paper, we propose a novel technique - that we call "Short-Dot" - to introduce redundant computations in a coding theory inspired fashion, for computing linear transforms of long vectors. Instead of computing long dot products as required in the original linear transform, we construct a larger number of redundant and short dot products that can be computed more efficiently at individual processors. Further, only a subset of these short dot products are required at the fusion node to finish the computation successfully. We demonstrate through probabilistic analysis as well as experiments on computing clusters that Short-Dot offers significant speed-up compared to existing techniques. We also derive trade-offs between the length of the dot-products and the resilience to stragglers (number of processors required to finish), for any such strategy and compare it to that achieved by our strategy.

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network. We propose a novel graphical model, namely Latent Differential Graph Model, where the networks under two different conditions are represented by two semiparametric elliptical distributions respectively, and the variation of these two networks (i.e., differential graph) is characterized by the difference between their latent precision matrices. We propose an estimator for the differential graph based on quasi likelihood maximization with nonconvex regularization. We show that our estimator attains a faster statistical rate in parameter estimation than the state-of-the-art methods, and enjoys oracle property under mild conditions. Thorough experiments on both synthetic and real world data support our theory.

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.

Probabilistic inference serves as a popular model for neural processing. It is still unclear, however, how approximate probabilistic inference can be accurate and scalable to very high-dimensional continuous latent spaces. Especially as typical posteriors for sensory data can be expected to exhibit complex latent dependencies including multiple modes. Here, we study an approach that can efficiently be scaled while maintaining a richly structured posterior approximation under these conditions. As example model we use spike-and-slab sparse coding for V1 processing, and combine latent subspace selection with Gibbs sampling (select-and-sample). Unlike factored variational approaches, the method can maintain large numbers of posterior modes and complex latent dependencies. Unlike pure sampling, the method is scalable to very high-dimensional latent spaces. Among all sparse coding approaches with non-trivial posterior approximations (MAP or ICA-like models), we report the largest-scale results. In applications we firstly verify the approach by showing competitiveness in standard denoising benchmarks. Secondly, we use its scalability to, for the first time, study highly-overcomplete settings for V1 encoding using sophisticated posterior representations. More generally, our study shows that very accurate probabilistic inference for multi-modal posteriors with complex dependencies is tractable, functionally desirable and consistent with models for neural inference.

We investigate active learning with access to two distinct oracles: LABEL (which is standard) and SEARCH (which is not). The SEARCH oracle models the situation where a human searches a database to seed or counterexample an existing solution. SEARCH is stronger than LABEL while being natural to implement in many situations. We show that an algorithm using both oracles can provide exponentially large problem-dependent improvements over LABEL alone.

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

Neural networks augmented with external memory have the ability to learn algorithmic solutions to complex tasks. These models appear promising for applications such as language modeling and machine translation. However, they scale poorly in both space and time as the amount of memory grows --- limiting their applicability to real-world domains. Here, we present an end-to-end differentiable memory access scheme, which we call Sparse Access Memory (SAM), that retains the representational power of the original approaches whilst training efficiently with very large memories. We show that SAM achieves asymptotic lower bounds in space and time complexity, and find that an implementation runs $1,\!000\times$ faster and with $3,\!000\times$ less physical memory than non-sparse models. SAM learns with comparable data efficiency to existing models on a range of synthetic tasks and one-shot Omniglot character recognition, and can scale to tasks requiring $100,\!000$s of time steps and memories. As well, we show how our approach can be adapted for models that maintain temporal associations between memories, as with the recently introduced Differentiable Neural Computer.

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

We study the problem of efficiently estimating the coefficients of generalized linear models (GLMs) in the large-scale setting where the number of observations $n$ is much larger than the number of predictors $p$, i.e. $n\gg p \gg 1$. We show that in GLMs with random (not necessarily Gaussian) design, the GLM coefficients are approximately proportional to the corresponding ordinary least squares (OLS) coefficients. Using this relation, we design an algorithm that achieves the same accuracy as the maximum likelihood estimator (MLE) through iterations that attain up to a cubic convergence rate, and that are cheaper than any batch optimization algorithm by at least a factor of $\mathcal{O}(p)$. We provide theoretical guarantees for our algorithm, and analyze the convergence behavior in terms of data dimensions. % Finally, we demonstrate the performance of our algorithm through extensive numerical studies on large-scale real and synthetic datasets, and show that it achieves the highest performance compared to several other widely used optimization algorithms.

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of AdaGrad is expected to attain better performance, however in high dimensions it is computationally impractical. We present Ada-LR and RadaGrad two computationally efficient approximations to full-matrix AdaGrad based on randomized dimensionality reduction. They are able to capture dependencies between features and achieve similar performance to full-matrix AdaGrad but at a much smaller computational cost. We show that the regret of Ada-LR is close to the regret of full-matrix AdaGrad which can have an up-to exponentially smaller dependence on the dimension than the diagonal variant. Empirically, we show that Ada-LR and RadaGrad perform similarly to full-matrix AdaGrad. On the task of training convolutional neural networks as well as recurrent neural networks, RadaGrad achieves faster convergence than diagonal AdaGrad.

The goal of minimizing misclassification error on a training set is often just one of several real-world goals that might be defined on different datasets. For example, one may require a classifier to also make positive predictions at some specified rate for some subpopulation (fairness), or to achieve a specified empirical recall. Other real-world goals include reducing churn with respect to a previously deployed model, or stabilizing online training. In this paper we propose handling multiple goals on multiple datasets by training with dataset constraints, using the ramp penalty to accurately quantify costs, and present an efficient algorithm to approximately optimize the resulting non-convex constrained optimization problem. Experiments on both benchmark and real-world industry datasets demonstrate the effectiveness of our approach.

Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming.