With the overwhelming online products available in recent years, there is an increasing need to filter and deliver relevant personalized advice for users. Recommender systems solve this problem by modeling and predicting individual preferences for a great variety of items such as movies, books or research articles. In this chapter, we explore rigorous network-based models that outperform leading approaches for recommendation. The network models we consider are based on the explicit assumption that there are groups of individuals and of items, and that the preferences of an individual for an item are determined only by their group memberships. The accurate prediction of individual user preferences over items can be accomplished by different methodologies, such as Monte Carlo sampling or Expectation-Maximization methods, the latter resulting in a scalable algorithm which is suitable for large datasets.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate that the {\sc BregmanTron} substantially outperforms the {\sc SLIsotron}, and that the loss it learns can be minimized by other algorithms for different tasks, thereby opening the interesting problem of \textit{loss transfer} between domains.

Tree-based algorithms for supervised learning, such as Classification and Regression Trees (CART) (Breiman et al., 1984), random forests (Breiman, 1996, 2001), adaBoost (Freund and Schapire, 1997), and gradient boosting (Breiman, 1997; Friedman, 2001, 2002), are widely used for applied supervised learning. As a whole, these methods are popular in applied settings due to their speed and accuracy in mean estimation and out-of-sample prediction tasks. One limitation of such methods is their well-known sensitivity to tuning parameters, which require costly cross-validation to optimize. Bayesian additive regression trees (BART) (Chipman et al., 2007, 2010) is a popular model-based alternative that is often more accurate than other treebased methods; specifically, BART boasts valuable robustness to the choice of tuning-parameters. However, relative to random forests and boosting, BART's wider adoption has been slowed by its more severe computational demands, owing to its reliance on a random walk Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm. Despite this limitation, BART has inspired a considerable body of research in recent years.

Let's review the concepts underlying Bayesian statistical analysis by walking through a simple classification model. The data come from the 1988 Bangladesh Fertility Survey, where 1934 observations were taken from women in urban and rural areas. The authors of the dataset, Mn and Cleland aimed to determine trends and causes of fertility as well as differences in fertility and child mortality. We will use the data in order to train a Bayesian logistic regression model that can predict if a given woman uses contraception. The dataset is well suited to Bayesian logistic regression because being able to quantify uncertainty when analyzing fertility is the major component of population dynamics that decide the size, structure, and composition of populations (source 1, source 2).

Image data has been greatly produced by individuals and commercial vendors in the daily life, and it has been used across various domains, like advertising, medical and traffic analysis. Recently, image data also appears to be greatly important in social utility, like emergency response. However, the privacy concern becomes the biggest obstacle that prevents further exploration of image data, due to that the image could reveal sensitive information, like the personal identity and locations. The recent developed Local Differential Privacy (LDP) brings us a promising solution, which allows the data owners to randomly perturb their input to provide the plausible deniability of the data before releasing. In this paper, we consider a two-party image classification problem, in which data owners hold the image and the untrustworthy data user would like to fit a machine learning model with these images as input. To protect the image privacy, we propose to locally perturb the image representation before revealing to the data user. Subsequently, we analyze how the perturbation satisfies {\epsilon}-LDP and affect the data utility regarding count-based and distance-based machine learning algorithm, and propose a supervised image feature extractor, DCAConv, which produces an image representation with scalable domain size. Our experiments show that DCAConv could maintain a high data utility while preserving the privacy regarding multiple image benchmark datasets.

Overfitting and treatment of "small data" are among the most challenging problems in the machine learning (ML), when a relatively small data statistics size $T$ is not enough to provide a robust ML fit for a relatively large data feature dimension $D$. Deploying a massively-parallel ML analysis of generic classification problems for different $D$ and $T$, existence of statistically-significant linear overfitting barriers for common ML methods is demonstrated. For example, these results reveal that for a robust classification of bioinformatics-motivated generic problems with the Long Short-Term Memory deep learning classifier (LSTM) one needs in a best case a statistics $T$ that is at least 13.8 times larger then the feature dimension $D$. It is shown that this overfitting barrier can be breached at a $10^{-12}$ fraction of the computational cost by means of the entropy-optimal Scalable Probabilistic Approximations algorithm (eSPA), performing a joint solution of the entropy-optimal Bayesian network inference and feature space segmentation problems. Application of eSPA to experimental single cell RNA sequencing data exhibits a 30-fold classification performance boost when compared to standard bioinformatics tools - and a 7-fold boost when compared to the deep learning LSTM classifier.

Bayesian reinforcement learning (BRL) offers a decision-theoretic solution to the problem of reinforcement learning. However, typical model-based BRL algorithms have focused either on ma intaining a posterior distribution on models or value functions and combining this with approx imate dynamic programming or tree search. This paper describes a novel backwards induction pri nciple for performing joint Bayesian estimation of models and value functions, from which many new BRL algorithms can be obtained. We demonstrate this idea with algorithms and experiments in discrete state spaces.

Machine Learning Lecture at CMU by Ke Li, Ph.D. Candidate at the University of California, Berkeley Lecturer: Ke Li Carnegie Mellon University Abstract: In this talk, Li presents his team's work on overcoming two long-standing problems in machine learning and algorithms: 1. Mode collapse in generative adversarial nets (GANs) Generative adversarial nets (GANs) are perhaps the most popular class of generative models in use today. Unfortunately, they suffer from the well-documented problem of mode collapse, which the many successive variants of GANs have failed to overcome. I will illustrate why mode collapse happens fundamentally and show a simple way to overcome it, which is the basis of a new method known as Implicit Maximum Likelihood Estimation (IMLE). It turns out that this problem is not insurmountable - I will explain how the curse of dimensionality arises and show a simple way to overcome it, which gives rise to a new family of algorithms known as Dynamic Continuous Indexing (DCI). Bio: Ke Li is a recent Ph.D. graduate from UC Berkeley, where he was advised by Prof. Jitendra Malik, and will join Google as a Research Scientist and the Institute for Advanced Study (IAS) as a Member hosted by Prof. Sanjeev Arora.

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient MCMC lgoriathm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional MCMC algorithms. The proposed algorithms have much alleviated the pain of Bayesian methods in big data computing.

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a curious experimental finding that suggests instead restricting the variational distribution to a more compact parameterization. For a variety of deep Bayesian neural networks trained using Gaussian mean-field variational inference, we find that the posterior standard deviations consistently exhibit strong low-rank structure after convergence. This means that by decomposing these variational parameters into a low-rank factorization, we can make our variational approximation more compact without decreasing the models' performance. Furthermore, we find that such factorized parameterizations improve the signal-to-noise ratio of stochastic gradient estimates of the variational lower bound, resulting in faster convergence.