A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are assumed to be induced by latent continuous variables corresponding to the grades assigned by the expert and the user to the objects. The dependence between the expert and user grades is modelled by a copula in some parametric family. Given a prior distribution on the copula parameter, the user's complete ranking is predicted by the mode of the posterior predictive distribution of the user's complete ranking conditional on the expert's complete and the user's incomplete rankings. Various Markov chain Monte-Carlo algorithms are proposed to approximate the predictive distribution or only its mode. The predictive distribution can be obtained exactly for the Farlie-Gumbel-Morgenstern copula family, providing a benchmark for the approximation accuracy of the algorithms. The method is applied to the MovieLens 100k dataset with a Gaussian copula modelling dependence between the expert's and user's grades.

Consider a left-truncated right-censored survival process whose evolution depends on time-varying covariates. Given functional data samples from the process, we propose a practical boosting procedure for estimating its log-intensity function. Our method does not require any separability assumptions like Cox proportional- or Aalen additive-hazards, thus it can flexibly capture time-covariate interactions. The estimator is consistent if the model is correctly specified; alternatively an oracle inequality can be demonstrated for tree-based models. We use the procedure to shed new light on a question from the operations literature concerning the effect of workload on service rates in an emergency department.

Graphical models provide a powerful framework for reasoning under uncertainty, and an influence diagram (ID) is a graphical model of a sequential decision problem that maximizes the total expected utility of a non-forgetting agent. Relaxing the regular modeling assumptions, an ID can be flexibly extended to general decision scenarios involving a limited memory agent or multi-agents. The approach of probabilistic planning with IDs is expected to gain computational leverage by exploiting the local structure as well as representation flexibility of influence diagram frameworks. My research focuses on graphical model inference for IDs and its application to probabilistic planning, targeting online MDP/POMDP planning as testbeds in the evaluation.

A multivariate Hawkes process is a class of marked point processes: A sample consists of a finite set of events of unbounded random size; each event has a real-valued time and a discrete-valued label (mark). It is self-excitatory: Each event causes an increase in the rate of other events (of either the same or a different label) in the (near) future. Prior work has developed methods for parameter estimation from complete samples. However, just as unobserved variables can increase the modeling power of other probabilistic models, allowing unobserved events can increase the modeling power of point processes. In this paper we develop a method to sample over the posterior distribution of unobserved events in a multivariate Hawkes process. We demonstrate the efficacy of our approach, and its utility in improving predictive power and identifying latent structure in real-world data.

Marginal MAP is a key task in Bayesian inference and decision-making. It is known to be very difficult in general, particularly because the evaluation of each MAP assignment requires solving an internal summation problem. In this paper, we propose a best-first search algorithm that provides anytime upper bounds for marginal MAP in graphical models. It folds the computation of external maximization and internal summation into an AND/OR tree search framework, and solves them simultaneously using a unified best-first search algorithm. The algorithm avoids some unnecessary computation of summation sub-problems associated with MAP assignments, and thus yields significant time savings. Furthermore, our algorithm is able to operate within limited memory. Empirical evaluation on three challenging benchmarks demonstrates that our unified best-first search algorithm using pre-compiled variational heuristics often provides tighter anytime upper bounds compared to those state-of-the-art baselines.

TD(0) is one of the most commonly used algorithms in reinforcement learning. Despite this, there is no existing finite sample analysis for TD(0) with function approximation, even for the linear case. Our work is the first to provide such results. Existing convergence rates for Temporal Difference (TD) methods apply only to somewhat modified versions, e.g., projected variants or ones where stepsizes depend on unknown problem parameters. Our analyses obviate these artificial alterations by exploiting strong properties of TD(0). We provide convergence rates both in expectation and with high-probability. The two are obtained via different approaches that use relatively unknown, recently developed stochastic approximation techniques.

Generating plausible and fluent sentence with desired properties has long been a challenge. Most of the recent works use recurrent neural networks (RNNs) and their variants to predict following words given previous sequence and target label. In this paper, we propose a novel framework to generate constrained sentences via Gibbs Sampling. The candidate sentences are revised and updated iteratively, with sampled new words replacing old ones. Our experiments show the effectiveness of the proposed method to generate plausible and diverse sentences.

The determinantal point process (DPP) has been receiving increasing attention in machine learning as a generative model of subsets consisting of relevant and diverse items. Recently, there has been a significant progress in developing efficient algorithms for learning the kernel matrix that characterizes a DPP. Here, we propose a dynamic DPP, which is a DPP whose kernel can change over time, and develop efficient learning algorithms for the dynamic DPP. In the dynamic DPP, the kernel depends on the subsets selected in the past, but we assume a particular structure in the dependency to allow efficient learning. We also assume that the kernel has a low rank and exploit a recently proposed learning algorithm for the DPP with low-rank factorization, but also show that its bottleneck computation can be reduced from O ( M 2 K ) time to O ( M K 2 ) time, where M is the number of items under consideration, and K is the rank of the kernel, which can be set smaller than M by orders of magnitude.

Learning an optimal policy from a multi-modal reward function is a challenging problem in reinforcement learning (RL). Hierarchical RL (HRL) tackles this problem by learning a hierarchicalpolicy, where multiple option policies are in charge of different strategies corresponding to modes of a reward function and a gating policy selects the best option for a given context. Although HRL has been demonstrated to be promising, current state-of-the-art methods cannot still perform well in complex real-world problems due to the difficulty of identifying modes of the reward function. In this paper, we propose a novel method called hierarchical policy search via return-weighted density estimation (HPSDE), which can efficiently identify the modes through density estimation with return-weighted importance sampling. Our proposed method finds option policies corresponding to the modes of the return function and automatically determines the number and the location of option policies, which significantly reduces the burden of hyper-parameters tuning. Through experiments, we demonstrate that the proposed HPSDE successfully learns option policies corresponding to modes of the return function and that it can be successfully applied to a motion planning problem of a redundant robotic manipulator.

We investigate the relationship between conditional independence (CI) x ⊥  y | Z and the independence of two residuals x – E ( x | Z ) ⊥  –E ( y | Z ), where x and y are two random variables, and Z is a set of random variables. We show that if x, y and Z are generated by following linear structural equation model and all external influences follow Gaussian distributions, then x ⊥  y | Z if and only if x – E ( x | Z ) ⊥ y – E ( y | Z ). That is, the test of x ⊥  y | Z can be relaxed to a simpler unconditional independence test of x – E ( x | Z ) ⊥  y – E ( y | Z ). Furthermore, if all these external influences follow non-Gaussian distributions and the model satisfies structural faithfulness condition, then we have x ⊥  y | Z ⇔ x – E ( x | Z ) ⊥  y – E ( y | Z ). We apply the results above to the causal discovery problem, where the causal directions are generally determined by a set of V -structures and their consistent propagations, so CI test-based methods can return a set of Markov equivalence classes. We show that in linear non-Gaussian context, x – E ( x | Z ) ⊥  y – E ( y | Z ) ⇒ x – E ( x | Z ) ⊥  z or y – E ( y | Z ⊥  z (∀ z ∈  Z ) if Z is a minimal d -separator, which implies z causes x (or y ) if z directly connects to x (or y ). Therefore, we conclude that CIs have useful information for distinguishing Markov equivalence classes. In summary, compared with the existing discretization-based and kernel-based CI testing methods, the proposed method provides a simpler way to measure CI, which needs only one unconditional independence test and two regression operations. When being applied to causal discovery, it can find more causal relationships, which is experimentally validated.