Dynamic Programming (DP) over tree decompositions is a well-established method to solve problems - that are in general NP-hard - efficiently for instances of small treewidth. Experience shows that (i) heuristically computing a tree decomposition has negligible runtime compared to the DP step; and (ii) DP algorithms exhibit a high variance in runtime when using different tree decompositions; in fact, given an instance of the problem at hand, even decompositions of the same width might yield extremely diverging runtimes. We thus propose here a novel and general method that is based on selection of the best decomposition from an available pool of heuristically generated ones. For this purpose, we require machine learning techniques that provide automated selection based on features of the decomposition rather than on the actual problem instance. Thus, one main contribution of this work is to propose novel features for tree decompositions. Moreover, we report on extensive experiments in different problem domains which show a significant speedup when choosing the tree decomposition according to this concept over simply using an arbitrary one of the same width.

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique. Moreover, based on the local error bound condition, we establish the linear convergence of our method to obtain a stationary point of the nonconvex optimization. In particular, we prove that not only the sequence generated linearly converges to a stationary point of the problem, but also the corresponding sequence of objective values is linearly convergent. Finally, some numerical experiments demonstrate the effectiveness of our method. To the best of our knowledge, it is first proved that the accelerated SGD method converges linearly to the local minimum of the nonconvex optimization.

Our goal is to learn a semantic parser that maps natural language utterances into executable programs when only indirect supervision is available: examples are labeled with the correct execution result, but not the program itself. Consequently, we must search the space of programs for those that output the correct result, while not being misled by spurious programs: incorrect programs that coincidentally output the correct result. We connect two common learning paradigms, reinforcement learning (RL) and maximum marginal likelihood (MML), and then present a new learning algorithm that combines the strengths of both. The new algorithm guards against spurious programs by combining the systematic search traditionally employed in MML with the randomized exploration of RL, and by updating parameters such that probability is spread more evenly across consistent programs. We apply our learning algorithm to a new neural semantic parser and show significant gains over existing state-of-the-art results on a recent context-dependent semantic parsing task.

This paper considers the problem of decentralized optimization with a composite objective containing smooth and non-smooth terms. To solve the problem, a proximal-gradient scheme is studied. Specifically, the smooth and nonsmooth terms are dealt with by gradient update and proximal update, respectively. The studied algorithm is closely related to a previous decentralized optimization algorithm, PG-EXTRA [37], but has a few advantages. First of all, in our new scheme, agents use uncoordinated step-sizes and the stable upper bounds on step-sizes are independent from network topologies. The step-sizes depend on local objective functions, and they can be as large as that of the gradient descent. Secondly, for the special case without non-smooth terms, linear convergence can be achieved under the strong convexity assumption. The dependence of the convergence rate on the objective functions and the network are separated, and the convergence rate of our new scheme is as good as one of the two convergence rates that match the typical rates for the general gradient descent and the consensus averaging. We also provide some numerical experiments to demonstrate the efficacy of the introduced algorithms and validate our theoretical discoveries.

As a mentee in the ChiPy mentorship program I will be writing a few blog posts about my project -- which was to learn how to implement a couple machine learning algorithms for execution on the graphics card. In this blog post, I'll introduce a few concepts fundamental to machine learning using logistic regression as an example, as well as a code with simple implementation in Python and OpenCL interfaced with PyOpenCL. This post is intended for a broad audience; if you're completely new to machine learning it may be worthwhile to read the beginning and mess around with the code on your own. And if you have any feedback, good or bad, let me know! If you would like to see the code I'm using, you can take a look at my github repository. There are many cases where it feels natural to attempt to model the outcome of an event as the probability that the event occurs, as we often record the outcome of some event as binary data.

We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the "Whitened neural networks" model. We make the whitening process not only in feed-forward direction as in the original model, but also in the back-propagation phase. Its efficacy is shown by an application of this "Bidirectional whitened neural networks" model to a handwritten character recognition data (MNIST data).

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the minimax error rate that is sharp up to logarithmic factors. We also analyze the performance of two versions of a computationally efficient estimator, and establish their consistency for a large range of input parameters. Finally, we provide an exact algorithm for the noiseless problem and demonstrate its performance on an image point-cloud matching task. Our analysis also extends to datasets with outliers.

Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground set, they exhibit interesting properties such as negative correlation, and, unlike other models, have efficient algorithms for sampling. When applied to kernel methods in machine learning, DPPs favor subsets of the given data with more diverse features. However, many real-world applications require efficient algorithms to sample from DPPs with additional constraints on the subset, e.g., partition or matroid constraints that are important to ensure priors, resource or fairness constraints on the sampled subset. Whether one can efficiently sample from DPPs in such constrained settings is an important problem that was first raised in a survey of DPPs by \cite{KuleszaTaskar12} and studied in some recent works in the machine learning literature. The main contribution of our paper is the first resolution of the complexity of sampling from DPPs with constraints. We give exact efficient algorithms for sampling from constrained DPPs when their description is in unary. Furthermore, we prove that when the constraints are specified in binary, this problem is #P-hard via a reduction from the problem of computing mixed discriminants implying that it may be unlikely that there is an FPRAS. Our results benefit from viewing the constrained sampling problem via the lens of polynomials. Consequently, we obtain a few algorithms of independent interest: 1) to count over the base polytope of regular matroids when there are additional (succinct) budget constraints and, 2) to evaluate and compute the mixed characteristic polynomials, that played a central role in the resolution of the Kadison-Singer problem, for certain special cases.

We present a dynamic model selection approach for resource-constrained prediction. Given an input instance at test-time, a gating function identifies a prediction model for the input among a collection of models. Our objective is to minimize overall average cost without sacrificing accuracy. We learn gating and prediction models on fully labeled training data by means of a bottom-up strategy. Our novel bottom-up method is a recursive scheme whereby a high-accuracy complex model is first trained. Then a low-complexity gating and prediction model are subsequently learnt to adaptively approximate the high-accuracy model in regions where low-cost models are capable of making highly accurate predictions. We pose an empirical loss minimization problem with cost constraints to jointly train gating and prediction models. On a number of benchmark datasets our method outperforms state-of-the-art achieving higher accuracy for the same cost.

When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history tracks her choices, i.e. which item was chosen among a subset of offerings. A user's comparisons are observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's preference of an unseen item to be used in recommendation systems. This also allows one to compute similarities among users and items to be used for categorization and search. Motivated by the empirical successes of the MultiNomial Logit (MNL) model in marketing and transportation, and also more recent successes in word embedding and crowdsourced image embedding, we pose this problem as learning the MNL model parameters that best explains the data. We propose a convex optimization for learning the MNL model, and show that it is minimax optimal up to a logarithmic factor by comparing its performance to a fundamental lower bound. This characterizes the minimax sample complexity of the problem, and proves that the proposed estimator cannot be improved upon other than by a logarithmic factor. Further, the analysis identifies how the accuracy depends on the topology of sampling via the spectrum of the sampling graph. This provides a guideline for designing surveys when one can choose which items are to be compared. This is accompanies by numerical simulations on synthetic and real datasets confirming our theoretical predictions.