NeurIPS 2016 Papers

Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function may require training a model which may involve days or even weeks of computation. Most methods for this so-called “Bayesian optimization” only allow sequential exploration of the parameter space. However, it is often desirable to propose batches or sets of parameter values to explore simultaneously, especially when there are large parallel processing facilities at our disposal. Batch methods require modeling the interaction between the different evaluations in the batch, which can be expensive in complex scenarios. In this paper, we propose a new approach for parallelizing Bayesian optimization by modeling the diversity of a batch via Determinantal point processes (DPPs) whose kernels are learned automatically. This allows us to generalize a previous result as well as prove better regret bounds based on DPP sampling. Our experiments on a variety of synthetic and real-world robotics and hyper-parameter optimization tasks indicate that our DPP-based methods, especially those based on DPP sampling, outperform state-of-the-art methods.

One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization methods, the common practice in SGD is either to use a diminishing step size, or to tune a step size by hand, which can be time consuming in practice. In this paper, we propose to use the Barzilai-Borwein (BB) method to automatically compute step sizes for SGD and its variant: stochastic variance reduced gradient (SVRG) method, which leads to two algorithms: SGD-BB and SVRG-BB. We prove that SVRG-BB converges linearly for strongly convex objective functions. As a by-product, we prove the linear convergence result of SVRG with Option I proposed in [10], whose convergence result has been missing in the literature. Numerical experiments on standard data sets show that the performance of SGD-BB and SVRG-BB is comparable to and sometimes even better than SGD and SVRG with best-tuned step sizes, and is superior to some advanced SGD variants.

We develop a Bayesian model for decision-making under time pressure with endogenous information acquisition. In our model, the decision-maker decides when to observe (costly) information by sampling an underlying continuous-time stochastic process (time series) that conveys information about the potential occurrence/non-occurrence of an adverse event which will terminate the decision-making process. In her attempt to predict the occurrence of the adverse event, the decision-maker follows a policy that determines when to acquire information from the time series (continuation), and when to stop acquiring information and make a final prediction (stopping). We show that the optimal policy has a "rendezvous" structure, i.e. a structure in which whenever a new information sample is gathered from the time series, the optimal "date" for acquiring the next sample becomes computable. The optimal interval between two information samples balances a trade-off between the decision maker’s "surprise", i.e. the drift in her posterior belief after observing new information, and "suspense", i.e. the probability that the adverse event occurs in the time interval between two information samples. Moreover, we characterize the continuation and stopping regions in the decision-maker’s state-space, and show that they depend not only on the decision-maker’s beliefs, but also on the "context", i.e. the current realization of the time series.

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.

We consider a crowdsourcing model in which n workers are asked to rate the quality of n items previously generated by other workers. An unknown set of $\alpha n$ workers generate reliable ratings, while the remaining workers may behave arbitrarily and possibly adversarially. The manager of the experiment can also manually evaluate the quality of a small number of items, and wishes to curate together almost all of the high-quality items with at most an fraction of low-quality items. Perhaps surprisingly, we show that this is possible with an amount of work required of the manager, and each worker, that does not scale with n: the dataset can be curated with $\tilde{O}(1/\beta\alpha\epsilon^4)$ ratings per worker, and $\tilde{O}(1/\beta\epsilon^2)$ ratings by the manager, where $\beta$ is the fraction of high-quality items. Our results extend to the more general setting of peer prediction, including peer grading in online classrooms.

The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for computationally efficient recovery methods. As a consequence, even though it is in general NP-hard to check that RIP holds, there have been substantial efforts to find tractable proxies for it. These would allow the construction of RIP matrices and the polynomial-time verification of RIP given an arbitrary matrix. We consider the framework of average-case certifiers, that never wrongly declare that a matrix is RIP, while being often correct for random instances. While there are such functions which are tractable in a suboptimal parameter regime, we show that this is a computationally hard task in any better regime. Our results are based on a new, weaker assumption on the problem of detecting dense subgraphs.

Calcium imaging is an important technique for monitoring the activity of thousands of neurons simultaneously. As calcium imaging datasets grow in size, automated detection of individual neurons is becoming important. Here we apply a supervised learning approach to this problem and show that convolutional networks can achieve near-human accuracy and superhuman speed. Accuracy is superior to the popular PCA/ICA method based on precision and recall relative to ground truth annotation by a human expert. These results suggest that convolutional networks are an efficient and flexible tool for the analysis of large-scale calcium imaging data.

Reconstruction of neuroanatomy is a fundamental problem in neuroscience. Stochastic expression of colors in individual cells is a promising tool, although its use in the nervous system has been limited due to various sources of variability in expression. Moreover, the intermingled anatomy of neuronal trees is challenging for existing segmentation algorithms. Here, we propose a method to automate the segmentation of neurons in such (potentially pseudo-colored) images. The method uses spatio-color relations between the voxels, generates supervoxels to reduce the problem size by four orders of magnitude before the final segmentation, and is parallelizable over the supervoxels. To quantify performance and gain insight, we generate simulated images, where the noise level and characteristics, the density of expression, and the number of fluorophore types are variable. We also present segmentations of real Brainbow images of the mouse hippocampus, which reveal many of the dendritic segments.

We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time. Crucially, the model itself learns to choose the appropriate number of inference steps. We use this scheme to learn to perform inference in partially specified 2D models (variable-sized variational auto-encoders) and fully specified 3D models (probabilistic renderers). We show that such models learn to identify multiple objects - counting, locating and classifying the elements of a scene - without any supervision, e.g., decomposing 3D images with various numbers of objects in a single forward pass of a neural network at unprecedented speed. We further show that the networks produce accurate inferences when compared to supervised counterparts, and that their structure leads to improved generalization.

n this paper, we propose and study an Asynchronous parallel Greedy Coordinate Descent (Asy-GCD) algorithm for minimizing a smooth function with bounded constraints. At each iteration, workers asynchronously conduct greedy coordinate descent updates on a block of variables. In the first part of the paper, we analyze the theoretical behavior of Asy-GCD and prove a linear convergence rate. In the second part, we develop an efficient kernel SVM solver based on Asy-GCD in the shared memory multi-core setting. Since our algorithm is fully asynchronous---each core does not need to idle and wait for the other cores---the resulting algorithm enjoys good speedup and outperforms existing multi-core kernel SVM solvers including asynchronous stochastic coordinate descent and multi-core LIBSVM.

We consider the assortment optimization problem when customer preferences follow a mixture of Mallows distributions. The assortment optimization problem focuses on determining the revenue/profit maximizing subset of products from a large universe of products; it is an important decision that is commonly faced by retailers in determining what to offer their customers. There are two key challenges: (a) the Mallows distribution lacks a closed-form expression (and requires summing an exponential number of terms) to compute the choice probability and, hence, the expected revenue/profit per customer; and (b) finding the best subset may require an exhaustive search. Our key contributions are an efficiently computable closed-form expression for the choice probability under the Mallows model and a compact mixed integer linear program (MIP) formulation for the assortment problem.

In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of RNNs in general. Second, we propose three architecture complexity measures of RNNs: (a) the recurrent depth, which captures the RNN’s over-time nonlinear complexity, (b) the feedforward depth, which captures the local input-output nonlinearity (similar to the “depth” in feedforward neural networks (FNNs)), and (c) the recurrent skip coefficient which captures how rapidly the information propagates over time. We rigorously prove each measure’s existence and computability. Our experimental results show that RNNs might benefit from larger recurrent depth and feedforward depth. We further demonstrate that increasing recurrent skip coefficient offers performance boosts on long term dependency problems.

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family has been very popular in machine learning due to its “Occam’s razor” interpretation. Unfortunately, calculating the potentials in the maximum entropy distribution is intractable [BGS14]. We provide computationally efficient versions of this principle when the mean parameters are pairwise moments: we design distributions that approximately match given pairwise moments, while having entropy which is comparable to the maximum entropy distribution matching those moments. We additionally provide surprising applications of the approximate maximum entropy principle to designing provable variational methods for partition function calculations for Ising models without any assumptions on the potentials of the model. More precisely, we show that we can get approximation guarantees for the log-partition function comparable to those in the low-temperature limit, which is the setting of optimization of quadratic forms over the hypercube. ([AN06])

In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words -- i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the anchor word assumption. Reliable estimates of higher-order statistics are hard to obtain, however, and the identification of topics under those models hinges on uncorrelatedness of the topics, which can be unrealistic. This paper revisits topic modeling based on second-order moments, and proposes an anchor-free topic mining framework. The proposed approach guarantees the identification of the topics under a much milder condition compared to the anchor-word assumption, thereby exhibiting much better robustness in practice. The associated algorithm only involves one eigen-decomposition and a few small linear programs. This makes it easy to implement and scale up to very large problem instances. Experiments using the TDT2 and Reuters-21578 corpus demonstrate that the proposed anchor-free approach exhibits very favorable performance (measured using coherence, similarity count, and clustering accuracy metrics) compared to the prior art.

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-of-the-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it on a challenging protein data set.

In this work we analyze the class prediction of parallel randomized ensembles by majority voting as an urn model. For a given test instance, the ensemble can be viewed as an urn of marbles of different colors. A marble represents an individual classifier. Its color represents the class label prediction of the corresponding classifier. The sequential querying of classifiers in the ensemble can be seen as draws without replacement from the urn. An analysis of this classical urn model based on the hypergeometric distribution makes it possible to estimate the confidence on the outcome of majority voting when only a fraction of the individual predictions is known. These estimates can be used to speed up the prediction by the ensemble. Specifically, the aggregation of votes can be halted when the confidence in the final prediction is sufficiently high. If one assumes a uniform prior for the distribution of possible votes the analysis is shown to be equivalent to a previous one based on Dirichlet distributions. The advantage of the current approach is that prior knowledge on the possible vote outcomes can be readily incorporated in a Bayesian framework. We show how incorporating this type of problem-specific knowledge into the statistical analysis of majority voting leads to faster classification by the ensemble and allows us to estimate the expected average speed-up beforehand.

Due to the computational difficulty of performing MMSE (minimum mean squared error) inference, maximum a posteriori (MAP) is often used as a surrogate. However, the accuracy of MAP is suboptimal for high dimensional inference, where the number of model parameters is of the same order as the number of samples. In this work we demonstrate how MMSE performance is asymptotically achievable via optimization with an appropriately selected convex penalty and regularization function which are a smoothed version of the widely applied MAP algorithm. Our findings provide a new derivation and interpretation for recent optimal M-estimators discovered by El Karoui, et. al. PNAS 2013 as well as extending to non-additive noise models. We demonstrate the performance of these optimal M-estimators with numerical simulations. Overall, at the heart of our work is the revelation of a remarkable equivalence between two seemingly very different computational problems: namely that of high dimensional Bayesian integration, and high dimensional convex optimization. In essence we show that the former computationally difficult integral may be computed by solving the latter, simpler optimization problem.

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.

Fast algorithms for nearest neighbor (NN) search have in large part focused on L2 distance. Here we develop an approach for L1 distance that begins with an explicit and exact embedding of the points into L2. We show how this embedding can efficiently be combined with random projection methods for L2 NN search, such as locality-sensitive hashing or random projection trees. We rigorously establish the correctness of the methodology and show by experimentation that it is competitive in practice with available alternatives.