Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a single principle. However, this estimator often has high variance and requires a full model evaluation per data point, making this algorithm costly in large graphs. In this work, we address these problems by generalizing concepts from the reinforcement learning literature. We introduce the concepts of value functions, baselines and critics for arbitrary SCGs, and show how to use them to derive lower-variance gradient estimates from partial model evaluations, paving the way towards general and efficient credit assignment for gradient-based optimization. In doing so, we demonstrate how our results unify recent advances in the probabilistic inference and reinforcement learning literature.

Preprint submitted to January 8, 2019 the use of Expectation-Maximization (EM) algorithm [8] which allows to get the maximum likelihood estimators in various incomplete-data problems [21]. The theoretical guarantees of these methods ensuring the correct prediction of missing values or the correct estimation of some parameters of interest are only valid if some assumptions are made on how the data came to be missing. Rubin [31] introduced three types of missing-data mechanisms: (i) the restrictive assumptions of missing completely at random (MCAR) data, (ii) the missing at random (MAR) data, where the missing data may only depend on the observable variables, and (iii) the more general assumption of missing not at random (MNAR) data, i.e. when the unavailability of the data depends on the values of other variables and its own value. A classic example of MNAR data, which is the focus of the paper, is surveys where rich people would be less willing to disclose their income or where people would be less incline to answer sensitive questions on their addictive use. Another example would be the diagnosis of Alzheimer's disease, which can be made using a score obtained by the patient on a specific test. However, when a patient has the disease, he or she has difficulty answering questions and is more likely to abandon the test before it ends.

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media, and the design of novel materials, e.g., for energy storage. Most microscopic properties exhibit complex statistical correlations and geometric constraints, which presents challenges for the estimation of macroscopic quantities of interest (QoIs), e.g., in the context of global sensitivity analysis (GSA) of macroscopic QoIs with respect to microscopic material properties. We present a systematic way of building correlations into stochastic multiscale models through Bayesian networks. This allows us to construct the joint probability density function (PDF) of model parameters through causal relationships that emulate engineering processes, e.g., the design of hierarchical nanoporous materials. Such PDFs also serve as input for the forward propagation of parametric uncertainty; our findings indicate that the inclusion of causal relationships impacts predictions of macroscopic QoIs. To assess the impact of correlations and causal relationships between microscopic parameters on macroscopic material properties, we use a moment-independent GSA based on the differential mutual information. Our GSA accounts for the correlated inputs and complex non-Gaussian QoIs. The global sensitivity indices are used to rank the effect of uncertainty in microscopic parameters on macroscopic QoIs, to quantify the impact of causality on the multiscale model's predictions, and to provide physical interpretations of these results for hierarchical nanoporous materials.

Abstract--We prove that the marginals densities of a primal normal factor graph and the corresponding marginal densities of its dual normal factor graph are related via local mappings. The mapping relies on no assumptions on the size, on the topology, or on the parameters of the graphical model. The mapping provides us with a simple procedure to transform simultaneously the estimated marginals from one domain to the other, which is particularly useful when such computations can be carried out more efficiently in one of the domains. In the case of the Ising model, valid configurations in the dual normal factor graph of the model coincide with the terms that appear in the high-temperature series expansion of the partition function. The subgraphs-world process (as a rapidly mixing Markov chain) can therefore be employed to draw samples according to the global probability mass function of the dual normal factor graph of ferromagnetic Ising models.

In this paper, we explore the effectiveness of dynamic analysis techniques for identifying malware, using Hidden Markov Models (HMMs) and Profile Hidden Markov Models (PHMMs), both trained on sequences of API calls. We contrast our results to static analysis using HMMs trained on sequences of opcodes, and show that dynamic analysis achieves significantly stronger results in many cases. Furthermore, in contrasting our two dynamic analysis techniques, we find that using PHMMs consistently outperforms our analysis based on HMMs.

Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models leverage the power of neural networks to implicitly learn and represent probability models over complex images. We describe methods to extract explicit probability density estimates from GANs, and explore the properties of these image density functions. We perform sanity check experiments to provide evidence that these probabilities are reasonable. However, we also show that density functions of natural images are difficult to interpret and thus limited in use. We study reasons for this lack of interpretability, and show that we can get interpretability back by doing density estimation on latent representations of images.

A high-level machine learning library that allows you to build programs that learn from data using the PHP language. Machine learning is the process by which a computer program is able to progressively improve performance on a certain task through training and data without explicitly being programmed. There are two types of machine learning that Rubix supports out of the box, Supervised and Unsupervised. Machine learning projects typically begin with a question. For example, you might want to answer the question "who of my friends are most likely to stay married to their spouse?" One way to go about answering this question with machine learning would be to go out and ask a bunch of happily married and divorced couples the same set of questions about their partner and then use that data to build a model of what a successful marriage looks like. Later, you can use that model to make predictions based on the answers you get from your friends. Specifically, the answers you collect are ...

A new mechanism for efficiently solving the Markov decision processes (MDPs) is proposed in this paper. We introduce the notion of reachability landscape where we use the Mean First Passage Time (MFPT) as a means to characterize the reachability of every state in the state space. We show that such reachability characterization very well assesses the importance of states and thus provides a natural basis for effectively prioritizing states and approximating policies. Built on such a novel observation, we design two new algorithms -- Mean First Passage Time based Value Iteration (MFPT-VI) and Mean First Passage Time based Policy Iteration (MFPT-PI) -- that have been modified from the state-of-the-art solution methods. To validate our design, we have performed numerical evaluations in robotic decision-making scenarios, by comparing the proposed new methods with corresponding classic baseline mechanisms. The evaluation results showed that MFPT-VI and MFPT-PI have outperformed the state-of-the-art solutions in terms of both practical runtime and number of iterations. Aside from the advantage of fast convergence, this new solution method is intuitively easy to understand and practically simple to implement.

The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a lengthy set of variables in modern data analysis, especially when data are collected in some automatic ways. This kinds of datasets may not collected with a specific analysis target and usually contains redundant features, which have no contribution to a the current analysis task of interest. Variable selection is a common way to increase the ability of model interpretation and is popularly used with some parametric classification models. There is a lack of studies about variable selection in nonparametric classification models such as the density estimation-based methods and this is especially the case for multiple-class classification situations. In this study we study multiple-class classification problems using the thought of sparse non-parametric density estimation and propose a method for identifying high impacts variables for each class. We present the asymptotic properties and the computation procedure for the proposed method together with some suggested sample size. We also repost the numerical results using both synthesized and some real data sets.

Optimal decision making with limited or no information in stochastic environments where multiple agents interact is a challenging topic in the realm of artificial intelligence. Reinforcement learning (RL) is a popular approach for arriving at optimal strategies by predicating stimuli, such as the reward for following a strategy, on experience. RL is heavily explored in the single-agent context, but is a nascent concept in multiagent problems. To this end, I propose several principled model-free and partially model-based reinforcement learning approaches for several multiagent settings. In the realm of normative reinforcement learning, I introduce scalable extensions to Monte Carlo exploring starts for partially observable Markov Decision Processes (POMDP), dubbed MCES-P, where I expand the theory and algorithm to the multiagent setting. I first examine MCES-P with probably approximately correct (PAC) bounds in the context of multiagent setting, showing MCESP+PAC holds in the presence of other agents. I then propose a more sample-efficient methodology for antagonistic settings, MCESIP+PAC. For cooperative settings, I extend MCES-P to the Multiagent POMDP, dubbed MCESMP+PAC. I then explore the use of reinforcement learning as a methodology in searching for optima in realistic and latent model environments. First, I explore a parameterized Q-learning approach in modeling humans learning to reason in an uncertain, multiagent environment. Next, I propose an implementation of MCES-P, along with image segmentation, to create an adaptive team-based reinforcement learning technique to positively identify the presence of phenotypically-expressed water and pathogen stress in crop fields.