The family of Expectation-Maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the Distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called \emph{workers} and \emph{managers} for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a $\gamma$-fraction of the workers, where $\gamma$ is a fixed constant in $(0, 1]$. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings.

We present safe active incremental f eature selection (SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each iteration as in dynamic screening. Different from these existing screening methods, SAIF starts from a small number of features and incrementally recruits active features and updates the significantly reduced model. Hence, it is much more computationally efficient and scalable with the number of features. More critically, SAIF has the safe guarantee as it has the convergence guarantee to the optimal solution to the original full LASSO problem. Such an incremental procedure and theoretical convergence guarantee can be extended to fused LASSO problems. Compared with state-of-the-art screening methods as well as working set and homotopy methods, which may not always guarantee the optimal solution, SAIF can achieve superior or comparable efficiency and high scalability with the safe guarantee when facing extremely high dimensional data sets. Experiments with both synthetic and real-world data sets show that SAIF can be up to 50 times faster than dynamic screening, and hundreds of times faster than computing LASSO or fused LASSO solutions without screening.

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

Network analysis of human brain connectivity is critically important for understanding brain function and disease states. Embedding a brain network as a whole graph instance into a meaningful low-dimensional representation can be used to investigate disease mechanisms and inform therapeutic interventions. Moreover, by exploiting information from multiple neuroimaging modalities or views, we are able to obtain an embedding that is more useful than the embedding learned from an individual view. Therefore, multi-view multi-graph embedding becomes a crucial task. Currently, only a few studies have been devoted to this topic, and most of them focus on the vector-based strategy which will cause structural information contained in the original graphs lost. As a novel attempt to tackle this problem, we propose Multi-view Multi-graph Embedding (M2E) by stacking multi-graphs into multiple partially-symmetric tensors and using tensor techniques to simultaneously leverage the dependencies and correlations among multi-view and multi-graph brain networks. Extensive experiments on real HIV and bipolar disorder brain network datasets demonstrate the superior performance of M2E on clustering brain networks by leveraging the multi-view multi-graph interactions.

We introduce a novel method to learn a policy from unsupervised demonstrations of a process. Given a model of the system and a set of sequences of outputs, we find a policy that has a comparable performance to the original policy, without requiring access to the inputs of these demonstrations. We do so by first estimating the inputs of the system from observed unsupervised demonstrations. Then, we learn a policy by applying vanilla supervised learning algorithms to the (estimated)input-output pairs. For the input estimation, we present a new adaptive linear estimator (AdaL-IE) that explicitly trades-off variance and bias in the estimation. As we show empirically, AdaL-IE produces estimates with lower error compared to the state-of-the-art input estimation method, (UMV-IE) [Gillijns and De Moor, 2007]. Using AdaL-IE in conjunction with imitation learning enables us to successfully learn control policies that consistently outperform those using UMV-IE.

K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so our performance estimates are in fact stochastic, with variability that can be substantial for natural language processing tasks. We demonstrate that these unstable estimates cannot be relied upon for effective parameter tuning. The resulting tuned parameters are highly sensitive to how our data is partitioned, meaning that we often select sub-optimal parameter choices and have serious reproducibility issues. Instead, we propose to use the less variable J-K-fold CV, in which J independent K-fold cross validations are used to assess performance. Our main contributions are extending J-K-fold CV from performance estimation to parameter tuning and investigating how to choose J and K. We argue that variability is more important than bias for effective tuning and so advocate lower choices of K than are typically seen in the NLP literature, instead use the saved computation to increase J. To demonstrate the generality of our recommendations we investigate a wide range of case-studies: sentiment classification (both general and target-specific), part-of-speech tagging and document classification.

We aim to predict whether an employee of a company will leave or not, using the k-Nearest Neighbors algorithm. We use evaluation of employee performance, average monthly hours at work and number of years spent in the company, among others, as our features. Other approaches to this problem include the use of ANNs, decision trees and logistic regression. The dataset was split, using 70% for training the algorithm and 30% for testing it, achieving an accuracy of 94.32%.

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [9] for regression with convex non-linearities. Our main assumption, in addition to other mild statistical and computational assumptions, is availability of a certain approximation oracle for the average of the gradients of the observation functions at a ground truth. Under this assumption and using a PAC-Bayesian analysis we show that the proposed estimator produces an accurate estimate with high probability. As a concrete example, we study the proposed framework in the bilinear regression problem with Gaussian factors and quantify a sufficient sample complexity for exact recovery. Furthermore, we describe a computationally tractable scheme that provably produces the required approximation oracle in the considered bilinear regression problem.

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high-dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterpart, we propose a new regularization method that leverages the clustered nature of data that is often encountered in practice. Our theoretical results indicate that this method overcomes the curse of dimensionality. This theoretical guarantee is supported by numerical experiments on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data.

It is well known that, for most datasets, the use of large-size minibatches for Stochastic Gradient Descent (SGD) typically leads to slow convergence and poor generalization. On the other hand, large minibatches are of great practical interest as they allow for a better exploitation of modern GPUs. Previous literature on the subject concentrated on how to adjust the main SGD parameters (in particular, the learning rate) when using large minibatches. In this work we introduce an additional feature, that we call minibatch persistency, that consists in reusing the same minibatch for K consecutive SGD iterations. The computational conjecture here is that a large minibatch contains a significant sample of the training set, so one can afford to slightly overfitting it without worsening generalization too much. The approach is intended to speedup SGD convergence, and also has the advantage of reducing the overhead related to data loading on the internal GPU memory. We present computational results on CIFAR-10 with an AlexNet architecture, showing that even small persistency values (K=2 or 5) already lead to a significantly faster convergence and to a comparable (or even better) generalization than the standard "disposable minibatch" approach (K=1), in particular when large minibatches are used. The lesson learned is that minibatch persistency can be a simple yet effective way to deal with large minibatches.