Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from the posterior distribution of a machine learning (ML) model based on the input data and the prior distribution over the model parameters. However, these algorithms do not apply to the decentralized learning setting, when a network of agents are working collaboratively to learn the parameters of an ML model without sharing their individual data due to privacy reasons or communication constraints. We study two algorithms: Decentralized SGLD (DE-SGLD) and Decentralized SGHMC (DE-SGHMC) which are adaptations of SGLD and SGHMC methods that allow scaleable Bayesian inference in the decentralized setting. We show that when the posterior distribution is strongly log-concave, the iterates of these algorithms converge linearly to a neighborhood of the target distribution in the 2-Wasserstein metric. We illustrate the results for decentralized Bayesian linear regression and Bayesian logistic regression problems.

Human-centered collaborative systems require proactive robot behavior with precise timing, which in turn mandates awareness of human actions, state of the environment and the task being executed, [1-4]. Proactive robot behavior is achieved by (1) recognizing the current state of the human collaborator and the environment based on real-time observations, (2) human action prediction given the observations and the model of the task, and (3) generating robot actions in line with the prediction. Human action recognition may however be highly uncertain if the human collaborator is not executing a strictly defined task plan. This is true regardless of whether perception is based on motion-capture devices or image based pose estimation. For a robot to act in a proactive manner, while at the same time avoiding actions when the risk of making a mistake is too high, it is essential for the action-decision system to take this uncertainty into consideration. We therefore propose to train the perception system and the robot policy in an end-to-end fashion using reinforcement learning (RL). This is different from earlier studies in which human action recognition and prediction are typically decoupled from robot action policy training [3-7]. Our main objective is to improve the fluency in coordination between the human and robot partners by allowing the policy to explicitly weigh the benefits of timely actions to the risk of making a mistake when uncertainties are too high.

In today's ultra-competitive business universe, Probability and Statistics are the most important fields of study. That is because statistical research presents businesses with the data they need to make informed decisions in every business area, whether it is market research, product development, product launch timing, customer data analysis, sales forecast, or employee performance. But why do you need to master probability and statistics in Python? The course'Mastering Probability and Statistics in Python' is designed carefully to reflect the most in-demand skills that will help you in understanding the concepts and methodology with regards to Python. How is this course different? This course is designed for beginners, although we will go far deep gradually.

Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the difficulty of this combinatorial problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms that are often interpreted as coordinate descent on the dual LP. To achieve more desirable computational properties, a number of methods regularize the LP with an entropy term, leading to a class of smooth message passing algorithms with convergence guarantees. In this paper, we present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient methods. The proposed algorithms incorporate the familiar steps of standard smooth message passing algorithms, which can be viewed as coordinate minimization steps. We show that these accelerated variants achieve faster rates for finding $\epsilon$-optimal points of the unregularized problem, and, when the LP is tight, we prove that the proposed algorithms recover the true MAP solution in fewer iterations than standard message passing algorithms.

Complex applications such as big data analytics involve different forms of coupling relationships that reflect interactions between factors related to technical, business (domain-specific) and environmental (including socio-cultural and economic) aspects. There are diverse forms of couplings embedded in poor-structured and ill-structured data. Such couplings are ubiquitous, implicit and/or explicit, objective and/or subjective, heterogeneous and/or homogeneous, presenting complexities to existing learning systems in statistics, mathematics and computer sciences, such as typical dependency, association and correlation relationships. Modeling and learning such couplings thus is fundamental but challenging. This paper discusses the concept of coupling learning, focusing on the involvement of coupling relationships in learning systems. Coupling learning has great potential for building a deep understanding of the essence of business problems and handling challenges that have not been addressed well by existing learning theories and tools. This argument is verified by several case studies on coupling learning, including handling coupling in recommender systems, incorporating couplings into coupled clustering, coupling document clustering, coupled recommender algorithms and coupled behavior analysis for groups.

Intelligent Tutoring Systems (ITSs) have been developed to provide students with personalized learning experiences by adaptively generating learning paths optimized for each individual. Within the vast scope of ITS, score prediction stands out as an area of study that enables students to construct individually realistic goals based on their current position. Via the expected score provided by the ITS, a student can instantaneously compare one's expected score to one's actual score, which directly corresponds to the reliability that the ITS can instill. In other words, refining the precision of predicted scores strictly correlates to the level of confidence that a student may have with an ITS, which will evidently ensue improved student engagement. However, previous studies have solely concentrated on improving the performance of a prediction model, largely lacking focus on the benefits generated by its practical application. In this paper, we demonstrate that the accuracy of the score prediction model deployed in a real-world setting significantly impacts user engagement by providing empirical evidence. To that end, we apply a state-of-the-art deep attentive neural network-based score prediction model to Santa, a multi-platform English ITS with approximately 780K users in South Korea that exclusively focuses on the TOEIC (Test of English for International Communications) standardized examinations. We run a controlled A/B test on the ITS with two models, respectively based on collaborative filtering and deep attentive neural networks, to verify whether the more accurate model engenders any student engagement. The results conclude that the attentive model not only induces high student morale (e.g. higher diagnostic test completion ratio, number of questions answered, etc.) but also encourages active engagement (e.g. higher purchase rate, improved total profit, etc.) on Santa.

We present a novel analysis of the expected risk of weighted majority vote in multiclass classification. The analysis takes correlation of predictions by ensemble members into account and provides a bound that is amenable to efficient minimization, which yields improved weighting for the majority vote. We also provide a specialized version of our bound for binary classification, which allows to exploit additional unlabeled data for tighter risk estimation. In experiments, we apply the bound to improve weighting of trees in random forests and show that, in contrast to the commonly used first order bound, minimization of the new bound typically does not lead to degradation of the test error of the ensemble.

While current research has shown the importance of Multi-parametric MRI (mpMRI) in diagnosing prostate cancer (PCa), further investigation is needed for how to incorporate the specific structures of the mpMRI data, such as the regional heterogeneity and between-voxel correlation within a subject. This paper proposes a machine learning-based method for improved voxel-wise PCa classification by taking into account the unique structures of the data. We propose a multi-resolution modeling approach to account for regional heterogeneity, where base learners trained locally at multiple resolutions are combined using the super learner, and account for between-voxel correlation by efficient spatial Gaussian kernel smoothing. The method is flexible in that the super learner framework allows implementation of any classifier as the base learner, and can be easily extended to classifying cancer into more sub-categories. We describe detailed classification algorithm for the binary PCa status, as well as the ordinal clinical significance of PCa for which a weighted likelihood approach is implemented to enhance the detection of the less prevalent cancer categories. We illustrate the advantages of the proposed approach over conventional modeling and machine learning approaches through simulations and application to in vivo data.

Reinforcement learning studies sequential decision making problems where a learning agent repeatedly interacts with an environment and aims to improve her strategy over time based on the received feedback. One of the most fundamental tradeoffs in reinforcement learning theory is the exploration vs. exploitation tradeoff, that arises whenever the learner observes only partial feedback after each of her decisions, thus having to balance between exploring new strategies and exploiting those that are already known to perform well. The most basic and well-studied form of partial feedback is the so-called "bandit" feedback, where the learner only observes the cost of her chosen action on each decision round, while obtaining no information about the performance of other actions. Traditionally, the environment dynamics in reinforcement learning are modeled as a Markov Decision Process (MDP) with a finite number of possible states and actions. The MDP model has been studied and analyzed in numerous different settings and under various assumptions on the transition parameters, the nature of the reward functions, and the feedback model. Recently, a particular focus has been given to continuous state-action MDPs, and in particular, to a specific family of models in classic control where the state transition function is linear.

We are interested in how to design reinforcement learning agents that provably reduce the sample complexity for learning new tasks by transferring knowledge from previously-solved ones. The availability of solutions to related problems poses a fundamental trade-off: whether to seek policies that are expected to achieve high (yet sub-optimal) performance in the new task immediately or whether to seek information to quickly identify an optimal solution, potentially at the cost of poor initial behavior. In this work, we focus on the second objective when the agent has access to a generative model of state-action pairs. First, given a set of solved tasks containing an approximation of the target one, we design an algorithm that quickly identifies an accurate solution by seeking the state-action pairs that are most informative for this purpose. We derive PAC bounds on its sample complexity which clearly demonstrate the benefits of using this kind of prior knowledge. Then, we show how to learn these approximate tasks sequentially by reducing our transfer setting to a hidden Markov model and employing spectral methods to recover its parameters. Finally, we empirically verify our theoretical findings in simple simulated domains.