The interaction of multiple autonomous agents gives rise to highly dynamic and nondeterministic environments, contributing to the complexity in applications such as automated financial markets, smart grids, or robotics. Due to the sheer number of situations that may arise, it is not possible to foresee and program the optimal behaviour for all agents beforehand. Consequently, it becomes essential for the success of the system that the agents can learn their optimal behaviour and adapt to new situations or circumstances. The past two decades have seen the emergence of reinforcement learning, both in single and multi-agent settings, as a strong, robust and adaptive learning paradigm. Progress has been substantial, and a wide range of algorithms are now available. An important challenge in the domain of multi-agent learning is to gain qualitative insights into the resulting system dynamics. In the past decade, tools and methods from evolutionary game theory have been successfully employed to study multi-agent learning dynamics formally in strategic interactions. This article surveys the dynamical models that have been derived for various multi-agent reinforcement learning algorithms, making it possible to study and compare them qualitatively. Furthermore, new learning algorithms that have been introduced using these evolutionary game theoretic tools are reviewed. The evolutionary models can be used to study complex strategic interactions. Examples of such analysis are given for the domains of automated trading in stock markets and collision avoidance in multi-robot systems. The paper provides a roadmap on the progress that has been achieved in analysing the evolutionary dynamics of multi-agent learning by highlighting the main results and accomplishments.

In the era of deep learning several unsupervised models have been developed to capture the key features in unlabeled handwritten data. Popular among them is the Restricted Boltzmann Machines RBM. However, due to the novelty in handwritten multidialect data, the RBM may fail to generate an efficient representation. In this paper we propose a generative model, the Mode Synthesizing Machine MSM for on-line representation of real life handwritten multidialect language data. The MSM takes advantage of the hierarchical representation of the modes of a data distribution using a two-point error update to learn a sequence of representative multidialects in a generative way. Experiments were performed to evaluate the performance of the MSM over the RBM with the former attaining much lower error values than the latter on both independent and mixed data set.

Abstract--In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach. Many configurations for x and Γ(.) have been explored in the literature for this problem; however, one of the most useful ones is to have a sparse signal x and a linear Γ(.), i.e., y Γ(x) Φx. Compressive sensing (CS) [1]-[3] is a field that tries to solve this linear inverse problem in case that x has a sparse representation, i.e., there exists an N N basis matrix Ψ [ψ Department of Electrical and Computer Engineering Rice University Houston, TX 77005 (i) How to recover the signal x from a given measurement vector y and operator Γ(.)? (ii) How to design the measurement operator Γ(.)? (iii) If we are concerned with any type of structure, How could we find a representation in which the signal x has that structure? Although there has been a considerable progress in CS and particularly in the answers of aforementioned questions, our goal is to go beyond the state-of-the-art results.

This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast to previous works on subspace-based data representations, this paper focuses on the geometric structure of a union of subspaces (UoS). In this regard, it proposes a distributed algorithm---termed cloud K-SVD---for collaborative learning of a UoS structure underlying distributed data of interest. The goal of cloud K-SVD is to learn a common overcomplete dictionary at each individual site such that every sample in the distributed data can be represented through a small number of atoms of the learned dictionary. Cloud K-SVD accomplishes this goal without requiring exchange of individual samples between sites. This makes it suitable for applications where sharing of raw data is discouraged due to either privacy concerns or large volumes of data. This paper also provides an analysis of cloud K-SVD that gives insights into its properties as well as deviations of the dictionaries learned at individual sites from a centralized solution in terms of different measures of local/global data and topology of interconnections. Finally, the paper numerically illustrates the efficacy of cloud K-SVD on real and synthetic distributed data.

Most existing word embedding methods can be categorized into Neural Embedding Models and Matrix Factorization (MF)-based methods. However some models are opaque to probabilistic interpretation, and MF-based methods, typically solved using Singular Value Decomposition (SVD), may incur loss of corpus information. In addition, it is desirable to incorporate global latent factors, such as topics, sentiments or writing styles, into the word embedding model. Since generative models provide a principled way to incorporate latent factors, we propose a generative word embedding model, which is easy to interpret, and can serve as a basis of more sophisticated latent factor models. The model inference reduces to a low rank weighted positive semidefinite approximation problem. Its optimization is approached by eigendecomposition on a submatrix, followed by online blockwise regression, which is scalable and avoids the information loss in SVD. In experiments on 7 common benchmark datasets, our vectors are competitive to word2vec, and better than other MF-based methods.

Uncovering causal relationships in data is a major objective of data analytics. Causal relationships are normally discovered with designed experiments, e.g. randomised controlled trials, which, however are expensive or infeasible to be conducted in many cases. Causal relationships can also be found using some well designed observational studies, but they require domain experts' knowledge and the process is normally time consuming. Hence there is a need for scalable and automated methods for causal relationship exploration in data. Classification methods are fast and they could be practical substitutes for finding causal signals in data. However, classification methods are not designed for causal discovery and a classification method may find false causal signals and miss the true ones. In this paper, we develop a causal decision tree where nodes have causal interpretations. Our method follows a well established causal inference framework and makes use of a classic statistical test. The method is practical for finding causal signals in large data sets.

Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of misclassifying one specific class than the other. Neyman-Pearson (NP) paradigm was introduced in this context as a novel statistical framework for handling asymmetric type I/II error priorities. It seeks classifiers with a minimal type II error and a constrained type I error under a user specified level. This article is the first attempt to construct classifiers with guaranteed theoretical performance under the NP paradigm in high-dimensional settings. Based on the fundamental Neyman-Pearson Lemma, we used a plug-in approach to construct NP-type classifiers for Naive Bayes models. The proposed classifiers satisfy the NP oracle inequalities, which are natural NP paradigm counterparts of the oracle inequalities in classical binary classification. Besides their desirable theoretical properties, we also demonstrated their numerical advantages in prioritized error control via both simulation and real data studies.

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, which may potentially help in bridging sparse approximation based methods to the traditional total-variation minimization. Based on this, we introduce a sparsity based framework for solving overparameterized variational problems. The latter has been used to improve the estimation of optical flow and also for general denoising of signals and images. However, the recovery of the space varying parameters involved was not adequately addressed by traditional variational methods. We first demonstrate the efficiency of the new framework for one dimensional signals in recovering a piecewise linear and polynomial function. Then, we illustrate how the new technique can be used for denoising and segmentation of images.

We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC criteria but also extends the conventional criteria in a way that it can be applicable also to a sequence of sparse multinomial observations, where even within a same cluster, the number of multinomial trials may be different for different observations. In addition, as a preliminary estimation step to maximum likelihood estimation, and more generally, to maximum $L_{q}$ estimation, we propose to use reduced rank projection in combination with non-negative factorization. We motivate our approach by showing that our model selection criterion and preliminary estimation step yield consistent estimates under simplifying assumptions. We also illustrate our approach through numerical experiments using real and simulated data.

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admits significantly less efficient algorithms. This motivates the computational model of convex optimization, including the offline, online and stochastic settings, using a linear optimization oracle. In this computational model we give several new results that improve over the previous state-of-the-art. Our main result is a novel conditional gradient algorithm for smooth and strongly convex optimization over polyhedral sets that performs only a single linear optimization step over the domain on each iteration and enjoys a linear convergence rate. This gives an exponential improvement in convergence rate over previous results. Based on this new conditional gradient algorithm we give the first algorithms for online convex optimization over polyhedral sets that perform only a single linear optimization step over the domain while having optimal regret guarantees, answering an open question of Kalai and Vempala, and Hazan and Kale. Our online algorithms also imply conditional gradient algorithms for non-smooth and stochastic convex optimization with the same convergence rates as projected (sub)gradient methods.