Learning with sequential data is widely encountered in domains such as natural language processing, genomics, speech recognition, video processing, financial time series analysis, and so on. Recurrent neural networks (RNN) are a flexible class of sequential models which can memorize past information, and selectively pass it on across sequence steps on multiple scales. However, training RNNs is challenging in practice, and backpropagation suffers from exploding and vanishing gradients as the length of the training sequence grows. To overcome this, either RNNs are trained over short sequences or incorporate more complex architectures such as long short-term memories (LSTM). For a detailed overview of RNNs, see [20]. Figure 1 contrasts the RNN with a feedforward neural network which has no memory. On the theoretical front, understanding of RNNs is at best rudimentary. With the current techniques, it is not tractable to analyze the highly nonlinear state evolution in RNNs. Analysis of backpropagation is also intractable due to non-convexity of the loss function, and in general, reaching the global optimum is hard. Here, we take the first steps towards addressing these challenging issues.

Unavoidable dead-ends are common in many probabilistic planning problems, e.g. when actions may fail or when operating under resource constraints. An important objective in such settings is MaxProb, determining the maximal probability with which the goal can be reached, and a policy achieving that probability. Yet algorithms for MaxProb probabilistic planning are severely underexplored, to the extent that there is scant evidence of what the empirical state of the art actually is. We close this gap with a comprehensive empirical analysis. We design and explore a large space of heuristic search algorithms, systematizing known algorithms and contributing several new algorithm variants. We consider MaxProb, as well as weaker objectives that we baptize AtLeastProb (requiring to achieve a given goal probabilty threshold) and ApproxProb (requiring to compute the maximum goal probability up to a given accuracy). We explore both the general case where there may be 0-reward cycles, and the practically relevant special case of acyclic planning, such as planning with a limited action-cost budget. We design suitable termination criteria, search algorithm variants, dead-end pruning methods using classical planning heuristics, and node selection strategies. We design a benchmark suite comprising more than 1000 instances adapted from the IPPC, resource-constrained planning, and simulated penetration testing. Our evaluation clarifies the state of the art, characterizes the behavior of a wide range of heuristic search algorithms, and demonstrates significant benefits of our new algorithm variants.

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, which is not necessarily reflected in similar behaviours at the level of trajectories. We propose a way to coarsen the state-space of a system which optimally preserves the satisfaction of a set of logical specifications about the system's trajectories. Our approach is based on Gaussian Process emulation and Multi-Dimensional Scaling, a dimensionality reduction technique which optimally preserves distances in non-Euclidean spaces. We show how to obtain low-dimensional visualisations of the system's state-space from the perspective of properties' satisfaction, and how to define macro-states which behave coherently with respect to the specifications. Our approach is illustrated on a non-trivial running example, showing promising performance and high computational efficiency.

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

We propose and study a new model for reinforcement learning with rich observations, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal of achieving long-term performance competitive with a large set of policies. To avoid barriers to sample-efficient learning associated with large observation spaces and general POMDPs, we focus on problems that can be summarized by a small number of hidden states and have long-term rewards that are predictable by a reactive function class. In this setting, we design and analyze a new reinforcement learning algorithm, Least Squares Value Elimination by Exploration. We prove that the algorithm learns near optimal behavior after a number of episodes that is polynomial in all relevant parameters, logarithmic in the number of policies, and independent of the size of the observation space. Our result provides theoretical justification for reinforcement learning with function approximation.

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing work focuses on the convergence of the objective function or the error of the obtained solution, we investigate the problem of statistical inference of the true model parameters based on SGD. To this end, we propose two consistent estimators of the asymptotic covariance of the average iterate from SGD: (1) an intuitive plug-in estimator and (2) a computationally more efficient batch-means estimator, which only uses the iterates from SGD. As the SGD process forms a time-inhomogeneous Markov chain, our batch-means estimator with carefully chosen increasing batch sizes generalizes the classical batch-means estimator designed for time-homogenous Markov chains. The proposed batch-means estimator is of independent interest, which can be potentially used for estimating the covariance of other time-inhomogeneous Markov chains. Both proposed estimators allow us to construct asymptotically exact confidence intervals and hypothesis tests. We further discuss an extension to conducting inference based on SGD for high-dimensional linear regression. Using a variant of the SGD algorithm, we construct a debiased estimator of each regression coefficient that is asymptotically normal. This gives a one-pass algorithm for computing both the sparse regression coefficient estimator and confidence intervals, which is computationally attractive and applicable to online data.

Interfacing a kinetic action of a person to an action of a machine system is an important research topic in many application areas. One of the key factors for intimate human-machine interaction is the ability of the control algorithm to detect and classify different user commands with shortest possible latency, thus making a highly correlated link between cause and effect. In our research, we focused on the task of mapping user kinematic actions into sound samples. The presented methodology relies on the wireless sensor nodes equipped with inertial measurement units and the real-time algorithm dedicated for early detection and classification of a variety of movements/gestures performed by a user. The core algorithm is based on the approximate Bayesian inference of Vector Autoregressive Hierarchical Hidden Markov Models (VAR-HHMM), where models database is derived from the set of motion gestures. The performance of the algorithm was compared with an online version of the K-nearest neighbours (KNN) algorithm, where we used offline expert based classification as the benchmark. In almost all of the evaluation metrics (e.g. confusion matrix, recall and precision scores) the VAR-HHMM algorithm outperformed KNN. Furthermore, the VAR-HHMM algorithm, in some cases, achieved faster movement onset detection compared with the offline standard. The proposed concept, although envisioned for movement-to-sound application, could be implemented in other human-machine interfaces.

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings. Based on our optimizational formulation, we propose a flexible Bayesian posterior regularization framework which for the first time enables us to put regularization at the distribution level. We apply this method to nonparametric state-space filtering tasks with extremely nonlinear dynamics and show performance gains over all other baselines.

The following is a list of, mostly free, machine learning online courses for beginners. First, and arguably the most popular course on this list, Machine Learning provides a broad introduction to machine learning, data mining, and statistical pattern recognition. The course will also draw from numerous case studies and applications, so that you'll also learn how to apply learning algorithms to building smart robots (perception, control), text understanding (web search, anti-spam), computer vision, medical informatics, audio, database mining, and other areas. The course is 11 weeks long and averages a 4.9/5 user rating, currently. It is free to take, but you can pay $79 for a certificate upon course completion.

Today, we can store and process so much data that we have nearly captured reality; no more sampling biases/ errors or related issues - this is my definition of Big Data; not tera or peta bytes! If you have measured the entire population (or close to it) and not sample just a small fraction, resulting data is BIG Data! There ARE subtle technical differences but let us just call it "Analytics", at least in business applications! When you hear "dynamics", time always comes to mind first but it is only one of the many possibilities. Dynamics could be over any independent variable!