In Bayesian Deep Learning, distributions over the output of classification neural networks are approximated by first constructing a Gaussian distribution over the weights, then sampling from it to receive a distribution over the categorical output distribution. This is costly. We reconsider old work to construct a Dirichlet approximation of this output distribution, which yields an analytic map between Gaussian distributions in logit space and Dirichlet distributions (the conjugate prior to the categorical) in the output space. We argue that the resulting Dirichlet distribution has theoretical and practical advantages, in particular more efficient computation of the uncertainty estimate, scaling to large datasets and networks like ImageNet and DenseNet. We demonstrate the use of this Dirichlet approximation by using it to construct a lightweight uncertainty-aware output ranking for the ImageNet setup.

High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynamics, and then performing control directly in the latent space. To ensure the learned latent dynamics are predictive of next-observations, all existing LCE approaches decode back into the observation space and explicitly perform next-observation prediction---a challenging high-dimensional task that furthermore introduces a large number of nuisance parameters (i.e., the decoder) which are discarded during control. In this paper, we propose a novel information-theoretic LCE approach and show theoretically that explicit next-observation prediction can be replaced with predictive coding. We then use predictive coding to develop a decoder-free LCE model whose latent dynamics are amenable to locally-linear control. Extensive experiments on benchmark tasks show that our model reliably learns a controllable latent space that leads to superior performance when compared with state-of-the-art LCE baselines.

We propose a novel actor-critic, model-free reinforcement learning algorithm which employs a Bayesian method of parameter space exploration to solve environments. A Gaussian process is used to learn the expected return of a policy given the policy's parameters. The system is trained by updating the parameters using gradient descent on a new surrogate loss function consisting of the Proximal Policy Optimization 'Clipped' loss function and a bonus term representing the expected improvement acquisition function given by the Gaussian process. This new method is shown to be comparable to and at times empirically outperform current algorithms on environments that simulate robotic locomotion using the MuJoCo physics engine.

Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of the intractability of the resulting optimization problem, most BNNs are either sampled through Monte Carlo methods, or trained by minimizing a suitable Evidence Lower BOund (ELBO) on a variational approximation. In this paper, we propose a variant of the latter, wherein we replace the Kullback-Leibler divergence in the ELBO term with a Maximum Mean Discrepancy (MMD) estimator, inspired by recent work in variational inference. After motivating our proposal based on the properties of the MMD term, we proceed to show a number of empirical advantages of the proposed formulation over the state-of-the-art. In particular, our BNNs achieve higher accuracy on multiple benchmarks, including several image classification tasks. In addition, they are more robust to the selection of a prior over the weights, and they are better calibrated. As a second contribution, we provide a new formulation for estimating the uncertainty on a given prediction, showing it performs in a more robust fashion against adversarial attacks and the injection of noise over their inputs, compared to more classical criteria such as the differential entropy.

Symmetric property estimation is a fundamental and well studied problem in machine learning and statistics. In this problem, we are given n i.i.d samples from an unknown distribution 1 p and asked to estimate f(p), where f is a symmetric property (i.e. it does not depend on the labels of the symbols). Over the past few years, the computational and sample complexities for estimating many symmetric properties have been extensively studied. Estimators with optimal sample complexities have been obtained for several properties including entropy [VV11b, WY16a, JVHW15], distance to uniformity [VV11a, JHW16], and support [VV11b, WY15]. All aforementioned estimators were property specific and therefore, a natural question is to design a universal estimator. In [ADOS16], the authors showed that the distribution that maximizes the profile likelihood, i.e. the likelihood of the multiset of frequencies of elements in the sample, referred to as profile maximum likelihood (PML) distribution, can be used as a universal plugin estimator.

We consider online learning for episodic Markov decision processes (MDPs) with stochastic long-term budget constraints, which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, whereas both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the MDP is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ and the action space $\mathcal{A}$. In this work, we propose a new \emph{upper confidence primal-dual} algorithm, which only requires the trajectories sampled from the transition model. In particular, we prove that the proposed algorithm achieves $\tilde{\mathcal{O}}(L|\mathcal{S}|\sqrt{|\mathcal{A}|T})$ upper bounds of both the regret and the constraint violation, where $L$ is the length of each episode. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning, which demonstrates the power of "optimism in the face of uncertainty" in constrained online learning.

In many complex, real-world situations, problem solving and decision making require effective reasoning about causation and uncertainty. However, human reasoning in these cases is prone to confusion and error. Bayesian networks (BNs) are an artificial intelligence technology that models uncertain situations, supporting probabilistic and causal reasoning and decision making. However, to date, BN methodologies and software require significant upfront training, do not provide much guidance on the model building process, and do not support collaboratively building BNs. BARD (Bayesian ARgumentation via Delphi) is both a methodology and an expert system that utilises (1) BNs as the underlying structured representations for better argument analysis, (2) a multi-user web-based software platform and Delphi-style social processes to assist with collaboration, and (3) short, high-quality e-courses on demand, a highly structured process to guide BN construction, and a variety of helpful tools to assist in building and reasoning with BNs, including an automated explanation tool to assist effective report writing. The result is an end-to-end online platform, with associated online training, for groups without prior BN expertise to understand and analyse a problem, build a model of its underlying probabilistic causal structure, validate and reason with the causal model, and use it to produce a written analytic report. Initial experimental results demonstrate that BARD aids in problem solving, reasoning and collaboration.

We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a fixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.

In this article, we are going to discuss we difference between Artificial Intelligence, Machine Learning, and Deep Learning. Furthermore, we will address the question of why Deep Learning as a young emerging field is far superior to traditional Machine Learning. Artificial Intelligence, Machine Learning, and Deep Learning are popular buzzwords that everyone seems to use nowadays. But still, there is a big misconception among many people about the meaning of these terms. In the worst case, one may think that these terms describe the same thing -- which is simply false.

Machine learning paradigm is ruled by a simple theorem known as "No Free Lunch" theorem. According to this, there is no algorithm in ML which will work best for all the problems. To state, one can not conclude that SVM is a better algorithm than decision trees or linear regression. Selection of an algorithm is dependent on the problem at hand and other factors like the size and structure of the dataset. In this blog, we are going to look into the top machine learning algorithms. Regression is a method used to predict numerical numbers.