Learning dynamic models from observed data has been a central issue in many scientific studies or engineering tasks. The usual setting is that data are collected sequentially from trajectories of some dynamical system operation. In quite a few modern scientific modeling tasks, however, it turns out that reliable sequential data are rather difficult to gather, whereas out-of-order snapshots are much easier to obtain. Examples include the modeling of galaxies, chronic diseases such Alzheimer's, or certain biological processes. Existing methods for learning dynamic model from non-sequence data are mostly based on Expectation-Maximization, which involves non-convex optimization and is thus hard to analyze. Inspired by recent advances in spectral learning methods, we propose to study this problem from a different perspective: moment matching and spectral decomposition. Under that framework, we identify reasonable assumptions on the generative process of non-sequence data, and propose learning algorithms based on the tensor decomposition method [2] to provably recover firstorder Markov models and hidden Markov models. To the best of our knowledge, this is the first formal guarantee on learning from non-sequence data. Preliminary simulation results confirm our theoretical findings.

First-order Markov models have been successfully applied to many prob- lems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the first- order conditional independence assumptions are not satisfied, and as a re- sult the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that ex- plicitly takes into account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likeli- hood, and allows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models.

Tracking a car or a person in a city is crucial for urban safety management. How can we complete the task with minimal number of spatiotemporal searches from massive camera records? This paper proposes a strategy named IHMs (Intermediate Searching at Heuristic Moments): each step we figure out which moment is the best to search according to a heuristic indicator, then at that moment search locations one by one in descending order of predicted appearing probabilities, until a search hits; iterate this step until we get the object's current location. Five searching strategies are compared in experiments, and IHMs is validated to be most efficient, which can save up to 1/3 total costs. This result provides an evidence that "searching at intermediate moments can save cost".

I have been teaching courses on data mining for over 10 years. One of my favorite lectures focuses on the use of Markov Models for predictive analytics. I enjoy giving this lecture because it always triggers interesting reactions from my students. Since the lecture can be used to demonstrate advanced concepts (like Bayesian inference and probabilistic reasoning) as well as basic concepts (like conditional probability and statistical dependence), I use the lecture both in my graduate course and in my freshman class. I start the lecture by telling the students that I will show them how to predict the future with a cat.

Learning dynamic models from observed data has been a central issue in many scientific studies or engineering tasks. The usual setting is that data are collected sequentially from trajectories of some dynamical system operation. In quite a few modern scientific modeling tasks, however, it turns out that reliable sequential data are rather difficult to gather, whereas out-of-order snapshots are much easier to obtain. Examples include the modeling of galaxies, chronic diseases such Alzheimer's, or certain biological processes. Existing methods for learning dynamic model from non-sequence data are mostly based on Expectation-Maximization, which involves non-convex optimization and is thus hard to analyze. Inspired by recent advances in spectral learning methods, we propose to study this problem from a different perspective: moment matching and spectral decomposition. Under that framework, we identify reasonable assumptions on the generative process of non-sequence data, and propose learning algorithms based on the tensor decomposition method \cite{anandkumar2012tensor} to \textit{provably} recover first-order Markov models and hidden Markov models. To the best of our knowledge, this is the first formal guarantee on learning from non-sequence data. Preliminary simulation results confirm our theoretical findings.

First-order Markov models have been successfully applied to many problems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditional independence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takes into account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, and allows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximum likelihood estimation in a number of control problems where the MDP's parameters are estimated from data.

First-order Markov models have been successfully applied to many problems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditional independence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takes into account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, and allows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximum likelihood estimation in a number of control problems where the MDP's parameters are estimated from data.

First-order Markov models have been successfully applied to many problems, forexample in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditionalindependence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takesinto account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, andallows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximumlikelihood estimation in a number of control problems where the MDP's parameters are estimated from data.