A construct that has been receiving attention recently in reinforcement learning is stochastic factorization (SF), a particular case of non-negative factorization (NMF) in which the matrices involved are stochastic. The idea is to use SF to approximate the transition matrices of a Markov decision process (MDP). This is useful for two reasons. First, learning the factors of the SF instead of the transition matrices can reduce significantly the number of parameters to be estimated. Second, it has been shown that SF can be used to reduce the number of operations needed to compute an MDP's value function. Recently, an algorithm called expectation-maximization SF (EMSF) has been proposed to compute a SF directly from transitions sampled from an MDP. In this paper we take a closer look at EMSF. First, by exploiting the assumptions underlying the algorithm, we show that it is possible to reduce it to simple multiplicative update rules similar to the ones that helped popularize NMF. Second, we analyze the optimization process underlying EMSF and find that it minimizes a modified version of the Kullback-Leibler divergence that is particularly well-suited for learning a SF from data sampled from an arbitrary distribution. Third, we build on this improved understanding of EMSF to draw an interesting connection with NMF and probabilistic latent semantic analysis. We also exploit the simplified update rules to introduce a new version of EMSF that generalizes and significantly improves its precursor. This new algorithm provides a practical mechanism to control the trade-off between memory usage and computing time, essentially freeing the space complexity of EMSF from its dependency on the number of sample transitions. The algorithm can also compute its approximation incrementally, which makes it possible to use it concomitantly with the collection of data. This feature makes the new version of EMSF particularly suitable for online reinforcement learning. Empirical results support the utility of the proposed algorithm.

Spatial and temporal contextual information plays a key role for analyzing user behaviors, and is helpful for predicting where he or she will go next. With the growing ability of collecting information, more and more temporal and spatial contextual information is collected in systems, and the location prediction problem becomes crucial and feasible. Some works have been proposed to address this problem, but they all have their limitations. Factorizing Personalized Markov Chain (FPMC) is constructed based on a strong independence assumption among different factors, which limits its performance. Tensor Factorization (TF) faces the cold start problem in predicting future actions. Recurrent Neural Networks (RNN) model shows promising performance comparing with PFMC and TF, but all these methods have problem in modeling continuous time interval and geographical distance. In this paper, we extend RNN and propose a novel method called Spatial Temporal Recurrent Neural Networks (ST-RNN). ST-RNN can model local temporal and spatial contexts in each layer with time-specific transition matrices for different time intervals and distance-specific transition matrices for different geographical distances. Experimental results show that the proposed ST-RNN model yields significant improvements over the competitive compared methods on two typical datasets, i.e., Global Terrorism Database (GTD) and Gowalla dataset.

In this paper, we propose principled weight learning algorithms for Markov logic networks that can easily scale to much larger datasets and application domains than existing algorithms. The main idea in our approach is to use approximate counting techniques to substantially reduce the complexity of the most computation intensive sub-step in weight learning: computing the number of groundings of a first-order formula that evaluate to true given a truth assignment to all the random variables. We derive theoretical bounds on the performance of our new algorithms and demonstrate experimentally that they are orders of magnitude faster and achieve the same accuracy or better than existing approaches.

We propose a simple but effective unsupervised learning algorithm to detect a common activity (co-activity) from a set of videos, which is formulated using absorbing Markov chain in a principled way. In our algorithm, a complete multipartite graph is first constructed, where vertices correspond to subsequences extracted from videos using a temporal sliding window and edges connect between the vertices originated from different videos; the weight of an edge is proportional to the similarity between the features of two end vertices. Then, we extend the graph structure by adding edges between temporally overlapped subsequences in a video to handle variable-length co-activities using temporal locality, and create an absorbing vertex connected from all other nodes. The proposed algorithm identifies a subset of subsequences as co-activity by estimating absorption time in the constructed graph efficiently. The great advantage of our algorithm lies in the properties that it can handle more than two videos naturally and identify multiple instances of a co-activity with variable lengths in a video. Our algorithm is evaluated intensively in a challenging dataset and illustrates outstanding performance quantitatively and qualitatively.

This paper introduces an extension of the target surveillance problem in which the surveillance agent is exposed to an adversarial ballistic threat. The problem is formulated as a mixed observability Markov decision process (MOMDP), which is a factored variant of the partially observable Markov decision process, to account for state and dynamic uncertainties. The control policy resulting from solving the MOMDP aims to optimize the frequency of target observations and minimize exposure to the ballistic threat. The adversary’s behavior is modeled with a level-k policy, which is used to construct the state transition of the MOMDP. The approach is empirically evaluated against a MOMDP adversary and against a human opponent in a target surveillance computer game. The empirical results demonstrate that, on average, level 3 MOMDP policies outperform lower level reasoning policies as well as human players.

Recently, there is an increasing interest in solving sequential The shortest path routing (SPR) problem entails finding the decision making problems under uncertainty, such shortest path between two given vertices of the graph that as Markov decision processes (MDPs), partially observable minimizes the total sum of weights of the involved edges MDPs (POMDPs) and its multiagent variants using in the path (Dijkstra 1959; Cormen et al. 2001). Shortest the probabilistic inference based viewpoint (Toussaint and path based approaches have found several applications in Storkey 2006; Toussaint, Charlin, and Poupart 2008; Kumar diverse fields such as transportation models (Pallottino and and Zilberstein 2010; Ghosh, Kumar, and Varakantham Scutella 1998), telecommunication network design (Pioro et 2015; Kumar, Zilberstein, and Toussaint 2015). Our al. 2002) and in ecology for analyzing landscape connectivity approach for SPDM is different from such previous applications for conservation planning (Bunn, Urban, and Keitt 2012; of the LM framework for planning.

The qualitative problem is of great importance as in several applications it is The de facto model for dynamic systems with probabilistic required that the correct behavior happens with probability 1, and nondeterministic behavior are Markov decision processes e.g., in the analysis of randomized embedded schedulers, (MDPs) (Howard 1960). MDPs provide the appropriate the important question is whether every thread progresses model to solve control and probabilistic planning problems with probability 1. Also in applications where it might be (Filar and Vrieze 1997; Puterman 1994), where the nondeterminism sufficient that the correct behavior happens with probability represents the choice of the control actions for at least λ 1,the correct choice of the threshold λ can the controller (or planner), while the stochastic response of be still challenging, due to simplifications and imprecisions the system to control actions is represented by the probabilistic introduced during modeling.

We present a probabilistic generative model for inferring a description of coordinated, recursively structured group activities at multiple levels of temporal granularity based on observations of individuals’ trajectories. The model accommodates: (1) hierarchically structured groups, (2) activities that are temporally and compositionally recursive, (3) component roles assigning different subactivity dynamics to subgroups of participants, and (4) a nonparametric Gaussian Process model of trajectories. We present an MCMC sampling framework for performing joint inference over recursive activity descriptions and assignment of trajectories to groups, integrating out continuous parameters. We demonstrate the model’s expressive power in several simulated and complex real-world scenarios from the VIRAT and UCLA Aerial Event video data sets.

Time series modeling is an important problem with many applications in different domains. Here we consider discriminative learning from time series, where we seek to predict an output response variable based on time series input. We develop a method based on convolution kernels to model discriminative learning over streams of text. Our method outperforms competitive baselines in three synthetic and two real datasets, rumour frequency modeling and popularity prediction tasks.

Many natural and social phenomena can be modeled by interaction point processes (IPPs) (Diggle et al. 1994), stochastic point processes considering the interaction between points. In this paper, we propose the infinite branching model (IBM), a Bayesian statistical model that can generalize and extend some popular IPPs, e.g., Hawkes process (Hawkes 1971; Hawkes and Oakes 1974). It treats IPP as a mixture of basis point processes with the aid of a distance dependent prior over branching structure that describes the relationship between points. The IBM can estimate point event intensity, interaction mechanism and branching structure simultaneously. A generic Metropolis-within-Gibbs sampling method is also developed for model parameter inference. The experiments on synthetic and real-world data demonstrate the superiority of the IBM.