We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. The connection between the sufficient forecasting and the deep learning architecture is explicitly stated. The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.

We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then review our proposed algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior.

This paper defines adversarial reasoning as computational approaches to inferring and anticipating an enemy's perceptions, intents and actions. It argues that adversarial reasoning transcends the boundaries of game theory and must also leverage such disciplines as cognitive modeling, control theory, AI planning and others. To illustrate the challenges of applying adversarial reasoning to real-world problems, the paper explores the lessons learned in the CADET -- a battle planning system that focuses on brigade-level ground operations and involves adversarial reasoning. From this example of current capabilities, the paper proceeds to describe RAID -- a DARPA program that aims to build capabilities in adversarial reasoning, and how such capabilities would address practical requirements in Defense and other application areas.

We present a domain-general account of causation that applies to settings in which macro-level causal relations between two systems are of interest, but the relevant causal features are poorly understood and have to be aggregated from vast arrays of micro-measurements. Our approach generalizes that of Chalupka et al. (2015) to the setting in which the macro-level effect is not specified. We formalize the connection between micro- and macro-variables in such situations and provide a coherent framework describing causal relations at multiple levels of analysis. We present an algorithm that discovers macro-variable causes and effects from micro-level measurements obtained from an experiment. We further show how to design experiments to discover macro-variables from observational micro-variable data. Finally, we show that under specific conditions, one can identify multiple levels of causal structure. Throughout the article, we use a simulated neuroscience multi-unit recording experiment to illustrate the ideas and the algorithms.

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to the local geometry of parameter space. A second issue is overfitting, which is typically addressed by early stopping. However, recent work has demonstrated that Bayesian model averaging mitigates this problem. The posterior can be sampled by using Stochastic Gradient Langevin Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD methods inefficient. Here, we propose combining adaptive preconditioners with SGLD. In support of this idea, we give theoretical properties on asymptotic convergence and predictive risk. We also provide empirical results for Logistic Regression, Feedforward Neural Nets, and Convolutional Neural Nets, demonstrating that our preconditioned SGLD method gives state-of-the-art performance on these models.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target posterior distributions. As the number of variables in a continuous-time diffusion increases, its numerical approximation error becomes a practical bottleneck, so better use of a numerical integrator is desirable. To this end, we propose use of an efficient symmetric splitting integrator in mSGNHT, instead of the traditional Euler integrator. We demonstrate that the proposed scheme is more accurate, robust, and converges faster. These properties are demonstrated to be desirable in Bayesian deep learning. Extensive experiments on two canonical models and their deep extensions demonstrate that the proposed scheme improves general Bayesian posterior sampling, particularly for deep models.

We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature.

A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However, if there is an unmeasured time series $Z$ that influences $X$, then this approach can lead to wrong causal conclusions, i.e., distinct from those one would draw if one had additional information such as $Z$. In this paper we take a different approach: We assume that $X$ together with some hidden $Z$ forms a first order vector autoregressive (VAR) process with transition matrix $A$, and argue why it is more valid to interpret $A$ causally instead of $\hat{B}$. Then we examine under which conditions the most important parts of $A$ are identifiable or almost identifiable from only $X$. Essentially, sufficient conditions are (1) non-Gaussian, independent noise or (2) no influence from $X$ to $Z$. We present two estimation algorithms that are tailored towards conditions (1) and (2), respectively, and evaluate them on synthetic and real-world data. We discuss how to check the model using $X$.

Latent Variable Models (LVMs) are a large family of machine learning models providing a principled and effective way to extract underlying patterns, structure and knowledge from observed data. Due to the dramatic growth of volume and complexity of data, several new challenges have emerged and cannot be effectively addressed by existing LVMs: (1) How to capture long-tail patterns that carry crucial information when the popularity of patterns is distributed in a power-law fashion? (2) How to reduce model complexity and computational cost without compromising the modeling power of LVMs? (3) How to improve the interpretability and reduce the redundancy of discovered patterns? To addresses the three challenges discussed above, we develop a novel regularization technique for LVMs, which controls the geometry of the latent space during learning to enable the learned latent components of LVMs to be diverse in the sense that they are favored to be mutually different from each other, to accomplish long-tail coverage, low redundancy, and better interpretability. We propose a mutual angular regularizer (MAR) to encourage the components in LVMs to have larger mutual angles. The MAR is non-convex and non-smooth, entailing great challenges for optimization. To cope with this issue, we derive a smooth lower bound of the MAR and optimize the lower bound instead. We show that the monotonicity of the lower bound is closely aligned with the MAR to qualify the lower bound as a desirable surrogate of the MAR. Using neural network (NN) as an instance, we analyze how the MAR affects the generalization performance of NN. On two popular latent variable models --- restricted Boltzmann machine and distance metric learning, we demonstrate that MAR can effectively capture long-tail patterns, reduce model complexity without sacrificing expressivity and improve interpretability.

Active learning (AL) is a learning paradigm where an active learner has to train a model (e.g., a classifier) which is in principal trained in a supervised way, but in AL it has to be done by means of a data set with initially unlabeled samples. To get labels for these samples, the active learner has to ask an oracle (e.g., a human expert) for labels. The goal is to maximize the performance of the model and to minimize the number of queries at the same time. In this article, we first briefly discuss the state of the art and own, preliminary work in the field of AL. Then, we propose the concept of collaborative active learning (CAL). With CAL, we will overcome some of the harsh limitations of current AL. In particular, we envision scenarios where an expert may be wrong for various reasons, there might be several or even many experts with different expertise, the experts may label not only samples but also knowledge at a higher level such as rules, and we consider that the labeling costs depend on many conditions. Moreover, in a CAL process human experts will profit by improving their own knowledge, too.