In this post, we will see the main technical ideas in the analysis of the mixing time of evolutionary Markov chains introduced in a previous post. We start by introducing the notion of the expected motion of a stochastic process or a Markov chain. In the case of a finite population evolutionary Markov chain, the expected motion turns out to be a dynamical system which corresponds to the infinite population evolutionary dynamics with the same parameters. Surprisingly, we show that the limit sets of this dynamical system govern the mixing time of the Markov chain. In particular, if the underlying dynamical system has a unique stable fixed point (as in asexual evolution), then the mixing is fast and in the case of multiple stable fixed points (as in sexual evolution), the mixing is slow.

Exponential-family harmoniums (EFHs), which extend restricted Boltzmann machines (RBMs) from Bernoulli random variables to other exponential families (Welling et al., 2005), are generative models that can be trained with unsupervised-learning techniques, like contrastive divergence (Hinton et al., 2006; Hinton, 2002), as density estimators for static data. Methods for extending RBMs--and likewise EFHs--to data with temporal dependencies have been proposed previously (Sutskever and Hinton, 2007; Sutskever et al., 2009), the learning procedure being validated by qualitative assessment of the generative model. Here we propose and justify, from a very different perspective, an alternative training procedure, proving sufficient conditions for optimal inference under that procedure. The resulting algorithm can be learned with only forward passes through the data--backprop-through-time is not required, as in previous approaches. The proof exploits a recent result about information retention in density estimators (Makin and Sabes, 2015), and applies it to a "recurrent EFH" (rEFH) by induction. Finally, we demonstrate optimality by simulation, testing the rEFH: (1) as a filter on training data generated with a linear dynamical system, the position of which is noisily reported by a population of "neurons" with Poisson-distributed spike counts; and (2) with the qualitative experiments proposed by Sutskever et al. (2009).

The following interview is one of many included in the report. As part of our ongoing series of interviews surveying the frontiers of machine intelligence, I recently interviewed Brendan Frey. Frey is a co-founder of Deep Genomics, a professor at the University of Toronto and a co-founder of its Machine Learning Group, a senior fellow of the Neural Computation program at the Canadian Institute for Advanced Research, and a fellow of the Royal Society of Canada. His work focuses on using machine learning to understand the genome and to realize new possibilities in genomic medicine. Brendan Frey: I completed my Ph.D. with Geoff Hinton in 1997.

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels.

Human communication takes many forms, including speech, text and instructional videos. It typically has an underlying structure, with a starting point, ending, and certain objective steps between them. In this paper, we consider instructional videos where there are tens of millions of them on the Internet. We propose a method for parsing a video into such semantic steps in an unsupervised way. Our method is capable of providing a semantic "storyline" of the video composed of its objective steps. We accomplish this using both visual and language cues in a joint generative model. Our method can also provide a textual description for each of the identified semantic steps and video segments. We evaluate our method on a large number of complex YouTube videos and show that our method discovers semantically correct instructions for a variety of tasks.

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of episodes required to guarantee a certain performance with high probability (PAC guarantee). In this paper, we derive an upper PAC bound $\tilde O(\frac{|\mathcal S|^2 |\mathcal A| H^2}{\epsilon^2} \ln\frac 1 \delta)$ and a lower PAC bound $\tilde \Omega(\frac{|\mathcal S| |\mathcal A| H^2}{\epsilon^2} \ln \frac 1 {\delta + c})$ that match up to log-terms and an additional linear dependency on the number of states $|\mathcal S|$. The lower bound is the first of its kind for this setting. Our upper bound leverages Bernstein's inequality to improve on previous bounds for episodic finite-horizon MDPs which have a time-horizon dependency of at least $H^3$.

In the previous blog post, we discussed the nature of sequential data and why we need a robust separate modeling technique to analyze that data. Traditionally, people have been using Hidden Markov Models (HMMs) to analyze sequential data, so we will center the discussion around HMMs in this blog post. HMMs have been implemented for many tasks such as speech recognition, gesture recognition, part-of-speech tagging, and so on. But HMMs place a lot of restrictions as to how we can model our data. HMMs are definitely better than using classical machine learning techniques, but they don't fully cover the needs of all the modern data analysis.

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using Gaussian kernels for both least squares and quantile regression. It turns out that for i.i.d.~processes, our learning rates for ERM recover the optimal rates. On the other hand, for non-i.i.d.~processes including geometrically $\alpha$-mixing Markov processes, geometrically $\alpha$-mixing processes with restricted decay, $\phi$-mixing processes, and (time-reversed) geometrically $\mathcal{C}$-mixing processes, our learning rates for SVMs with Gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called "effective number of observations" for various mixing processes.

This sunday we are running a workshop at ACM CHI 2016 called "Human Centered Machine Learning". I thought I would write an article to explain the general idea (though the workshop itself is a way of better understanding the idea). Statistical Machine Learning is one of the most successful set of techniques to come out of Computer Science in the last decades, and one that a lot of people are thinking about at the moment. It's often presented as quite an impersonal process: machines that learn for themselves, even AI that risk taking over the world. But, in fact, there is a lot of human work that goes into machine learning and not enough people have been talking about that.

Data science and machine learning have long been interests of mine, but now that I'm working on Fuzzy.io I need to keep on top of all the news in both fields. My preferred way to do this is through listening to podcasts. I've listened to a bunch of machine learning and data science podcasts in the last few months, so I thought I'd share my favorites: Every other week, they release a 10–15 minute episode where hosts, Kyle and Linda Polich give a short primer on topics like k-means clustering, natural language processing and decision tree learning, often using analogies related to their pet parrot, Yoshi. This is the only place where you'll learn about k-means clustering via placement of parrot droppings.