This column is by Matt Fogel, Co-Founder, Fuzzy.io Data science and machine learning have long been interests of mine, but now that I'm working on Fuzzy.ai I need to keep on top of all the news in both fields. My preferred way to do this is through listening to podcasts. I've listened to a bunch of machine learning and data science podcasts in the last few months, so I thought I'd share my favorites: Every other week, they release a 10–15 minute episode where hosts, Kyle and Linda Polich give a short primer on topics like k-means clustering, natural language processing and decision tree learning, often using analogies related to their pet parrot, Yoshi.

While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence. The past few years have seen major advances in many perception tasks using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. To achieve integrated intelligence that involves both perception and inference, it is naturally desirable to tightly integrate deep learning and Bayesian models within a principled probabilistic framework, which we call Bayesian deep learning. In this unified framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in return, the feedback from the inference process is able to enhance the perception of text or images. This paper proposes a general framework for Bayesian deep learning and reviews its recent applications on recommender systems, topic models, and control. In this paper, we also discuss the relationship and differences between Bayesian deep learning and other related topics like Bayesian treatment of neural networks.

The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces the Bayesian SLOPE procedure for linear regression. The classical SLOPE estimate is the posterior mode in the normal regression problem with an appropriate prior on the coefficients. The Bayesian SLOPE considers the full Bayesian model and has the advantage of offering credible sets and standard error estimates for the parameters. Moreover, the hierarchical Bayesian framework allows for full Bayesian and empirical Bayes treatment of the penalty coefficients; whereas it is not clear how to choose these coefficients when using the SLOPE on a general design matrix. A direct characterization of the posterior is provided which suggests a Gibbs sampler that does not involve latent variables. An efficient hybrid Gibbs sampler for the Bayesian SLOPE is introduced. Point estimation using the posterior mean is highlighted, which automatically facilitates the Bayesian prediction of future observations. These are demonstrated on real and synthetic data.

In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classification allows the classifiers to output a set of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed classifiers build on and refine many existing single-label classifiers. The optimal classifier can sometimes output the empty set. We provide two solutions to fix this issue that are suitable for various practical needs.

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC as unknown parameters from measurements. Specifically, we focus on single linkage hierarchical clustering (SLHC) and study its geometry. We prove that under fairly reasonable conditions on the probability distribution governing measurements, SLHC is equivalent to maximum partial profile likelihood estimation (MPPLE) with some of the information contained in the data ignored. At the same time, we show that direct evaluation of SLHC on maximum likelihood estimation (MLE) of pairwise distances yields a consistent estimator. Consequently, a full MLE is expected to perform better than SLHC in getting the correct HC results for the ground truth metric.

A Markov chain is a random process with the property that the next state depends only on the current state. For example: If you have the choice of red or blue twice the process would be Markovian if each time you chose the decision had nothing to do with your choice previously (see diagram below). How can Markov Chains help us? To start with we need to define some basic terminology. The changes of state within the system are called transitions, and the probabilities associated with various state-changes are called transition probabilities.

Last summer, I was at a conference having lunch with Hal Daume III when we got to talking about how "Bayesian" can be a funny and ambiguous term. It seems like the definition should be straightforward: "following the work of English mathematician Rev. Thomas Bayes," perhaps, or even "uses Bayes' theorem." But many methods bearing the reverend's name or using his theorem aren't even considered "Bayesian" by his most religious followers. Why is it that Bayesian networks, for example, aren't considered… y'know… Bayesian? As I've read more outside the fields of machine learning and natural language processing -- from psychometrics and environmental biology to hackers who dabble in data science -- I've noticed three distinct uses of the term "Bayesian."

My 2 month summer internship at Skymind (the company behind the open source deeplearning library DL4J) comes to an end and this is a post to summarize what I have been working on: Building a deep reinforcement learning library for DL4J: … (drums roll) … RL4J! This post begins by an introduction to reinforcement learning and is then followed by a detailed explanation of DQN (Deep Q-Network) for pixel inputs and is concluded by an RL4J example. I will assume from the reader some familiarity with neural networks. But first, lets talk about the core concepts of reinforcement learning. A "simple aspect of science" may be defined as one which, through good fortune, I happen to understand. Reinforcement Learning is an exciting area of machine learning. It is basically the learning of an efficient strategy in a given environment. Informally, this is very similar to Pavlovian conditioning: you assign a reward for a given behavior and over time, the agents learn to reproduce that behavior in order to receive more rewards. It is an iterative trial and error process. Formally, an environment is defined as a Markov Decision Process (MDP). Note: It is usually more convenient to use the set of Action \(A_s\) which is the set of available move from a given state, than the complete set A. \(A_s\) is simply the elements \(a\) in \(A\) such that \(P(s' s, a) 0\).

Prof. Bostrom has written a book that I believe will become a classic within that subarea of Artificial Intelligence (AI) concerned with the existential dangers that could threaten humanity as the result of the development of artificial forms of intelligence. What fascinated me is that Bostrom has approached the existential danger of AI from a perspective that, although I am an AI professor, I had never really examined in any detail. When I was a graduate student in the early 80s, studying for my PhD in AI, I came upon comments made in the 1960s (by AI leaders such as Marvin Minsky and John McCarthy) in which they mused that, if an artificially intelligent entity could improve its own design, then that improved version could generate an even better design, and so on, resulting in a kind of "chain-reaction explosion" of ever-increasing intelligence, until this entity would have achieved "superintelligence". This chain-reaction problem is the one that Bostrom focusses on. He sees three main paths to superintelligence: 1. The AI path -- In this path, all current (and future) AI technologies, such as machine learning, Bayesian networks, artificial neural networks, evolutionary programming, etc. are applied to bring about a superintelligence.

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.