Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent Indian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly modeling the connectivity structure of groups. We demonstrate our model's capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction.

We introduce a class of models for multidimensional control problems which we call skip-free Markov decision processes on trees. We describe and analyse an algorithm applicable to Markov decision processes of this type that are skip-free in the negative direction. Starting with the finite average cost case, we show that the algorithm combines the advantages of both value iteration and policy iteration -- it is guaranteed to converge to an optimal policy and optimal value function after a finite number of iterations but the computational effort required for each iteration step is comparable with that for value iteration. We show that the algorithm can also be used to solve discounted cost models and continuous time models, and that a suitably modified algorithm can be used to solve communicating models.

Crowdsourcing requesters are trapped between a rock and a hard place. Typically they specify their crowdsourcing workflows procedurally, but current languages commit them to overly strict and static policies that waste human effort. While optimizing workflows with more sophisticated tools like POMDPs can significantly reduce labor costs, such advanced AI techniques are hard to use and understand. We report on our progress in developing Clowder, a system that provides the user with an adaptive programming language that looks and feels like Lisp, yet abstracts over POMDPs so that non-experts can write POMDPs without knowing anything about them. Such a system frees requesters from needing to resort to suboptimal techniques that use approximate heuristics or hire a planning expert to formally define and solve their problems.

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward-backward (F-B) algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming algorithms that, we collectively call $k$-segment algorithms, that allow us to i) find MAP sequences, ii) compute posterior probabilities and iii) simulate sample paths conditional on a user specified number of segments, i.e. contiguous runs in a hidden state, possibly of a particular type. We illustrate the utility of these methods using simulated and real examples and highlight the application of prospective and retrospective use of these methods for fitting HMMs or exploring existing model fits.

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

Concept-to-text generation refers to the task of automatically producing textual output from non-linguistic input. We present a joint model that captures content selection ("what to say") and surface realization ("how to say") in an unsupervised domain-independent fashion. Rather than breaking up the generation process into a sequence of local decisions, we define a probabilistic context-free grammar that globally describes the inherent structure of the input (a corpus of database records and text describing some of them). We recast generation as the task of finding the best derivation tree for a set of database records and describe an algorithm for decoding in this framework that allows to intersect the grammar with additional information capturing fluency and syntactic well-formedness constraints. Experimental evaluation on several domains achieves results competitive with state-of-the-art systems that use domain specific constraints, explicit feature engineering or labeled data.

We devise a USDCHF trading strategy using the dynamics of gold as a filter. Our strategy involves modelling both USDCHF and gold using a coupled hidden Markov model (CHMM). The observations will be indicators, RSI and CCI, which will be used as triggers for our trading signals. Upon decoding the model in each iteration, we can get the next most probable state and the next most probable observation. Hopefully by taking advantage of intermarket analysis and the Markov property implicit in the model, trading with these most probable values will produce profitable results.

This paper considers a transmission control problem in network-coded two-way relay channels (NC-TWRC), where the relay buffers random symbol arrivals from two users, and the channels are assumed to be fading. The problem is modeled by a discounted infinite horizon Markov decision process (MDP). The objective is to find a transmission control policy that minimizes the symbol delay, buffer overflow and transmission power consumption and error rate simultaneously and in the long run. By using the concepts of submodularity, multimodularity and L-natural convexity, we study the structure of the optimal policy searched by dynamic programming (DP) algorithm. We show that the optimal transmission policy is nondecreasing in queue occupancies or/and channel states under certain conditions such as the chosen values of parameters in the MDP model, channel modeling method, modulation scheme and the preservation of stochastic dominance in the transitions of system states. The results derived in this paper can be used to relieve the high complexity of DP and facilitate real-time control.

Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced by Airoldi et al. This model allows for nodes to have fractional memberships in multiple communities and assumes that the community memberships are drawn from a Dirichlet distribution. Moreover, it contains the stochastic block model as a special case. We propose a unified approach to learning these models via a tensor spectral decomposition method. Our estimator is based on low-order moment tensor of the observed network, consisting of 3-star counts. Our learning method is fast and is based on simple linear algebraic operations, e.g. singular value decomposition and tensor power iterations. We provide guaranteed recovery of community memberships and model parameters and present a careful finite sample analysis of our learning method. As an important special case, our results match the best known scaling requirements for the (homogeneous) stochastic block model.

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^{\gamma}$ for some $\gamma <1$ and each edge has a random edge weight in $[-1,1]$. Our algorithm learns {\em almost all} networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural networks with random edge weights.