We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they allow new components to be introduced on the fly as needed. This, however, posts an important challenge to distributed estimation -- how to handle new components efficiently and consistently. To tackle this problem, we propose a new estimation method, which allows new components to be created locally in individual computing nodes. Components corresponding to the same cluster will be identified and merged via a probabilistic consolidation scheme. In this way, we can maintain the consistency of estimation with very low communication cost. Experiments on large real-world data sets show that the proposed method can achieve high scalability in distributed and asynchronous environments without compromising the mixing performance.

These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant improvement over those given in our earlier work where this "correlated-PCA" problem was first studied. In fact, in certain regimes, our results imply that the sample complexity required to achieve subspace recovery error that is a constant fraction of the noise level is near-optimal. Useful corollaries of our result include guarantees for PCA in sparse data-dependent noise and for PCA with missing data. An important application of the former is in proving correctness of the subspace update step of a popular online algorithm for dynamic robust PCA.

Multi-task learning (MTL) has recently contributed to learning better representations in service of various NLP tasks. MTL aims at improving the performance of a primary task, by jointly training on a secondary task. This paper introduces automated tasks, which exploit the sequential nature of the input data, as secondary tasks in an MTL model. We explore next word prediction, next character prediction, and missing word completion as potential automated tasks. Our results show that training on a primary task in parallel with a secondary automated task improves both the convergence speed and accuracy for the primary task. We suggest two methods for augmenting an existing network with automated tasks and establish better performance in topic prediction, sentiment analysis, and hashtag recommendation. Finally, we show that the MTL models can perform well on datasets that are small and colloquial by nature.

Demand response (DR) is an important source of flexibility for the electric power grid [1], [2], [3]. In this work, we use online convex optimization (OCO) to design algorithms for tracking setpoints with uncertain flexible loads in DR programs. Uncertainty is a key challenge in DR [4]. This uncertainty arises from weather, human behavior and unknown load models. In addition, loads are time-varying, e.g., a heater may not have much flexibility during cold nights. The uncertain, time-varying nature of loads means that load aggregators must deploy loads for DR to observe their capabilities.

Trans-dimensional random field language models (TRF LMs) have recently been introduced, where sentences are modeled as a collection of random fields. The TRF approach has been shown to have the advantages of being computationally more efficient in inference than LSTM LMs with close performance and being able to flexibly integrating rich features. In this paper we propose neural TRFs, beyond of the previous discrete TRFs that only use linear potentials with discrete features. The idea is to use nonlinear potentials with continuous features, implemented by neural networks (NNs), in the TRF framework. Neural TRFs combine the advantages of both NNs and TRFs. The benefits of word embedding, nonlinear feature learning and larger context modeling are inherited from the use of NNs. At the same time, the strength of efficient inference by avoiding expensive softmax is preserved. A number of technical contributions, including employing deep convolutional neural networks (CNNs) to define the potentials and incorporating the joint stochastic approximation (JSA) strategy in the training algorithm, are developed in this work, which enable us to successfully train neural TRF LMs. Various LMs are evaluated in terms of speech recognition WERs by rescoring the 1000-best lists of WSJ'92 test data. The results show that neural TRF LMs not only improve over discrete TRF LMs, but also perform slightly better than LSTM LMs with only one fifth of parameters and 16x faster inference efficiency.

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear operator constraints. By modeling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.

In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient estimate and can easily make good use of parallel computing. The core of our proposed method is the incorporation of our new "double acceleration" technique and variance reduction technique. We theoretically analyze our proposed method and show that our method much improves the mini-batch efficiencies of previous accelerated stochastic methods, and essentially only needs size $\sqrt{n}$ mini-batches for achieving the optimal iteration complexities for both non-strongly and strongly convex objectives, where $n$ is the training set size. Further, we show that even in non-mini-batch settings, our method achieves the best known convergence rate for both non-strongly and strongly convex objectives.

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems.

In a seminal paper Abadie, Diamond, and Hainmueller [2010] (ADH), see also Abadie and Gardeazabal [2003], Abadie et al. [2014], develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units. The method constructs a set of weights such that selected covariates and pre-treatment outcomes of the treated unit are approximately matched by a weighted average of control units (the synthetic control). The weights are restricted to be nonnegative and sum to one, which is important because it allows the procedure to obtain unique weights even when the number of lagged outcomes is modest relative to the number of control units, a common setting in applications. In the current paper we propose a generalization that allows the weights to be negative, and their sum to differ from one, and that allows for a permanent additive difference between the treated unit and the controls, similar to difference-in-difference procedures. The weights directly minimize the distance between the lagged outcomes for the treated and the control units, using regularization methods to deal with a potentially large number of possible control units.

We introduce a deep learning architecture for structure-based virtual screening that generates fixed-sized fingerprints of proteins and small molecules by applying learnable atom convolution and softmax operations to each compound separately. These fingerprints are further transformed non-linearly, their inner-product is calculated and used to predict the binding potential. Moreover, we show that widely used benchmark datasets may be insufficient for testing structure-based virtual screening methods that utilize machine learning. Therefore, we introduce a new benchmark dataset, which we constructed based on DUD-E and PDBBind databases.