Link: Bayesian Machine Learning in Python: A/B Testing coupon code udemy Traditional A/B testing has been around for a long time, and it's full of approximations and confusing definitions. In this course, while we will do traditional A/B testing in order to appreciate its complexity, what we will eventually get to is the Bayesian machine learning way of doing things. First, we'll see if we can improve on ... Bestseller by Lazy Programmer Inc. What you'll learn Use adaptive algorithms to improve A/B testing performance Understand the difference between Bayesian and frequentist statistics Apply Bayesian methods to A/B testing Description This course is all about A/B testing. A/B testing is used everywhere.

The use of target networks is a common practice in deep reinforcement learning for stabilizing the training; however, theoretical understanding of this technique is still limited. In this paper, we study the so-called periodic Q-learning algorithm (PQ-learning for short), which resembles the technique used in deep Q-learning for solving infinite-horizon discounted Markov decision processes (DMDP) in the tabular setting. PQ-learning maintains two separate Q-value estimates - the online estimate and target estimate. The online estimate follows the standard Q-learning update, while the target estimate is updated periodically. In contrast to the standard Q-learning, PQ-learning enjoys a simple finite time analysis and achieves better sample complexity for finding an epsilon-optimal policy. Our result provides a preliminary justification of the effectiveness of utilizing target estimates or networks in Q-learning algorithms.

The success of neural networks in image classification has inspired various hardware implementations on embedded platforms such as Field Programmable Gate Arrays, embedded processors and Graphical Processing Units. These embedded platforms are constrained in terms of power, which is mainly consumed by the Multiply Accumulate operations and the memory accesses for weight fetching. Quantization and pruning have been proposed to address this issue. Though effective, these techniques do not take into account the underlying architecture of the embedded hardware. In this work, we propose PoET-BiN, a Look-Up Table based power efficient implementation on resource constrained embedded devices. A modified Decision Tree approach forms the backbone of the proposed implementation in the binary domain. A LUT access consumes far less power than the equivalent Multiply Accumulate operation it replaces, and the modified Decision Tree algorithm eliminates the need for memory accesses. We applied the PoET-BiN architecture to implement the classification layers of networks trained on MNIST, SVHN and CIFAR-10 datasets, with near state-of-the art results. The energy reduction for the classifier portion reaches up to six orders of magnitude compared to a floating point implementations and up to three orders of magnitude when compared to recent binary quantized neural networks.

Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either abandon the maximum-likelihood framework entirely, or else rely on a variety of variational approximations to the posterior distribution over the latents. Here, we propose an alternative approach that we call amortised learning. Rather than computing an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo strategy to learn a function that directly estimates the maximum-likelihood parameter updates. Amortised learning is possible whenever samples of latents and observations can be simulated from the generative model, treating the model as a "black box". We demonstrate its effectiveness on a wide range of complex models, including those with latents that are discrete or supported on non-Euclidean spaces.

We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCMC method. Instead of treating each parallel chain independently from others, our proposed algorithm implements a repulsive force between particles, avoiding collapse and facilitating a better exploration of the parameter space. We also show how the addition of this noise term is necessary to obtain a valid SG-MCMC sampler, a significant difference with SVGD. Experiments with both synthetic distributions and real datasets illustrate the benefits of the proposed scheme.

Likelihood-free inference for simulator-based statistical models has recently grown rapidly from its infancy to a useful tool for practitioners. However, models with more than a very small number of parameters as the target of inference have remained an enigma, in particular for the approximate Bayesian computation (ABC) community. To advance the possibilities for performing likelihood-free inference in high-dimensional parameter spaces, here we introduce an extension of the popular Bayesian optimisation based approach to approximate discrepancy functions in a probabilistic manner which lends itself to an efficient exploration of the parameter space. Our method achieves computational scalability by using separate acquisition procedures for the discrepancies defined for different parameters. These efficient high-dimensional simulation acquisitions are combined with exponentiated loss-likelihoods to provide a misspecification-robust characterisation of the marginal posterior distribution for all model parameters. The method successfully performs computationally efficient inference in a 100-dimensional space on canonical examples and compares favourably to existing Copula-ABC methods. We further illustrate the potential of this approach by fitting a bacterial transmission dynamics model to daycare centre data, which provides biologically coherent results on the strain competition in a 30-dimensional parameter space.

In this paper, we design a navigation policy for multiple unmanned aerial vehicles (UAVs) where mobile base stations (BSs) are deployed to improve the data freshness and connectivity to the Internet of Things (IoT) devices. First, we formulate an energy-efficient trajectory optimization problem in which the objective is to maximize the energy efficiency by optimizing the UAV-BS trajectory policy. We also incorporate different contextual information such as energy and age of information (AoI) constraints to ensure the data freshness at the ground BS. Second, we propose an agile deep reinforcement learning with experience replay model to solve the formulated problem concerning the contextual constraints for the UAV-BS navigation. Moreover, the proposed approach is well-suited for solving the problem, since the state space of the problem is extremely large and finding the best trajectory policy with useful contextual features is too complex for the UAV-BSs. By applying the proposed trained model, an effective real-time trajectory policy for the UAV-BSs captures the observable network states over time. Finally, the simulation results illustrate the proposed approach is 3.6% and 3.13% more energy efficient than those of the greedy and baseline deep Q Network (DQN) approaches.

We consider the problem of estimating a ranking on a set of items from noisy pairwise comparisons given item features. We address the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be compared based on only a salient subset of features. Formalizing this framework, we propose the "salient feature preference model" and prove a sample complexity result for learning the parameters of our model and the underlying ranking with maximum likelihood estimation. We also provide empirical results that support our theoretical bounds and illustrate how our model explains systematic intransitivity. Finally we demonstrate strong performance of maximum likelihood estimation of our model on both synthetic data and two real data sets: the UT Zappos50K data set and comparison data about the compactness of legislative districts in the US.

In this article, we describe the algorithms for causal structure learning from time series data that won the Causality 4 Climate competition at the Conference on Neural Information Processing Systems 2019 (NeurIPS). We examine how our combination of established ideas achieves competitive performance on semi-realistic and realistic time series data exhibiting common challenges in real-world Earth sciences data. In particular, we discuss a) a rationale for leveraging linear methods to identify causal links in non-linear systems, b) a simulation-backed explanation as to why large regression coefficients may predict causal links better in practice than small p-values and thus why normalising the data may sometimes hinder causal structure learning. For benchmark usage, we provide implementations at https://github.com/sweichwald/tidybench and detail the algorithms here. We propose the presented competition-proven methods for baseline benchmark comparisons to guide the development of novel algorithms for structure learning from time series.

This paper studies the statistical theory of batch data reinforcement learning with function approximation. Consider the off-policy evaluation problem, which is to estimate the cumulative value of a new target policy from logged history generated by unknown behavioral policies. We study a regression-based fitted Q iteration method, and show that it is equivalent to a model-based method that estimates a conditional mean embedding of the transition operator. We prove that this method is information-theoretically optimal and has nearly minimal estimation error. In particular, by leveraging contraction property of Markov processes and martingale concentration, we establish a finite-sample instance-dependent error upper bound and a nearly-matching minimax lower bound. The policy evaluation error depends sharply on a restricted $\chi^2$-divergence over the function class between the long-term distribution of the target policy and the distribution of past data. This restricted $\chi^2$-divergence is both instance-dependent and function-class-dependent. It characterizes the statistical limit of off-policy evaluation. Further, we provide an easily computable confidence bound for the policy evaluator, which may be useful for optimistic planning and safe policy improvement.