Data science is an interdisciplinary field. One of the building blocks of data science is statistics. Without a decent level of statistics knowledge, it would be highly difficult to understand or interpret the data. Statistics helps us explain the data. We use statistics to infer results about a population based on a sample drawn from that population.

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational inference or stochastic-gradient Markov chain Monte Carlo (SGMCMC). To investigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures. We show that (1) BNNs can achieve significant performance gains over standard training and deep ensembles; (2) a single long HMC chain can provide a comparable representation of the posterior to multiple shorter chains; (3) in contrast to recent studies, we find posterior tempering is not needed for near-optimal performance, with little evidence for a "cold posterior" effect, which we show is largely an artifact of data augmentation; (4) BMA performance is robust to the choice of prior scale, and relatively similar for diagonal Gaussian, mixture of Gaussian, and logistic priors; (5) Bayesian neural networks show surprisingly poor generalization under domain shift; (6) while cheaper alternatives such as deep ensembles and SGMCMC methods can provide good generalization, they provide distinct predictive distributions from HMC. Notably, deep ensemble predictive distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual-as well as in the group-sports. We show how the well-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data. In this work we are interested in the rating algorithms that can be systematically derived from the probabilistic models which describe i) how the the skills affect the outcomes of the games, as well as ii) how the skills evolve in time, i.e., characterize the skills dynamics. Using the probabilistic models, the forecasting of the game outcomes is naturally derived from the rating.

We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving Gaussian Processes with a distance-preserving affine operator on distributions. Our experiments on brain tissue-segmentation show that the resulting architecture approaches the performance of well-established deterministic segmentation algorithms (U-Net), which has never been achieved with previous hierarchical Gaussian Processes. Moreover, by applying the same segmentation model to out-of-distribution data (i.e., images with pathology such as brain tumors), we show that our uncertainty estimates result in out-of-distribution detection that outperforms the capabilities of previous Bayesian networks and reconstruction-based approaches that learn normative distributions.

In machine learning, ensemble methods [10] aim to combine hypotheses to make predictive models more robust and accurate. A weighted majority vote learning procedure is an ensemble method for classification where each voter/hypothesis is assigned a weight (i.e., its influence in the final voting). Among the most famous majority vote methods, we can cite Boosting [13], Bagging [5], or Random Forest [6]. Interestingly, most of the kernel-based classifiers, like Support Vector Machines [3, 7], can be seen as majority vote of kernel functions. Understanding when and why weighted majority votes perform better than a single hypothesis is challenging. To study the generalization abilities of such majority votes, the PAC-Bayesian framework [34, 25] offers powerful tools to obtain Probably Approximately Correct (PAC) generalization bounds. Motivated by the fact that PAC-Bayesian analyses can lead to tight bounds (see e.g., [28]), developing algorithms to minimize such bounds is an important direction (e.g., [14, 11, 15, 24]). We focus on a class of PAC-Bayesian algorithms minimizing an upper bound on the majority vote's risk called the C-Bound

Prediction of diabetes and its various complications has been studied in a number of settings, but a comprehensive overview of problem setting for diabetes prediction and care management has not been addressed in the literature. In this document we seek to remedy this omission in literature with an encompassing overview of diabetes complication prediction as well as situating this problem in the context of real world healthcare management. We illustrate various problems encountered in real world clinical scenarios via our own experience with building and deploying such models. In this manuscript we illustrate a Machine Learning (ML) framework for addressing the problem of predicting Type 2 Diabetes Mellitus (T2DM) together with a solution for risk stratification, intervention and management. These ML models align with how physicians think about disease management and mitigation, which comprises these four steps: Identify, Stratify, Engage, Measure.

Incrementally training deep neural networks to recognize new classes is a challenging problem. Most existing class-incremental learning methods store data or use generative replay, both of which have drawbacks, while 'rehearsal-free' alternatives such as parameter regularization or bias-correction methods do not consistently achieve high performance. Here, we put forward a new strategy for class-incremental learning: generative classification. Rather than directly learning the conditional distribution p(y|x), our proposal is to learn the joint distribution p(x,y), factorized as p(x|y)p(y), and to perform classification using Bayes' rule. As a proof-of-principle, here we implement this strategy by training a variational autoencoder for each class to be learned and by using importance sampling to estimate the likelihoods p(x|y). This simple approach performs very well on a diverse set of continual learning benchmarks, outperforming generative replay and other existing baselines that do not store data.

In every corner of machine learning and statistics, there is a need for estimators that work not just in an idealized model, but even when their assumptions are violated. Unfortunately, in high dimensions, being provably robust and being efficiently computable are often at odds with each other. We give the first efficient algorithm for estimating the parameters of a high-dimensional Gaussian that is able to tolerate a constant fraction of corruptions that is independent of the dimension. Prior to our work, all known estimators either needed time exponential in the dimension to compute or could tolerate only an inverse-polynomial fraction of corruptions. Not only does our algorithm bridge the gap between robustness and algorithms, but also it turns out to be highly practical in a variety of settings. Machine learning is filled with examples of estimators that work well in idealized settings but fail when their assumptions are violated. In fact, these are examples of a more general paradigm within statistics called maximum likelihood estimation: When we know the distribution comes from some parametric family, we choose the parameters that are the most likely to have generated the observed data. In 1922, Ronald Fisher12 formulated the maximum likelihood principle. It has many wonderful properties (under various technical conditions), such as converging to the true parameters as the number of samples goes to infinity, a property called consistency. Moreover, it has asymptotically the smallest possible variance among all unbiased estimators, a property called asymptotic consistency. In 1960, John Tukey24 challenged the conventional wisdom in parametric estimation by asking a simple question: Are there provably robust methods to estimate the parameters of a one-dimensional Gaussian?

High-dimensional limit theorems have been shown to be useful to derive tuning rules for finding the optimal scaling in random walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive; the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameter-dimension-dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target density is close to having a product form, but significantly different otherwise.

In this paper, we take a human-centered approach to interpretable machine learning. First, drawing inspiration from the study of explanation in philosophy, cognitive science, and the social sciences, we propose a list of design principles for machine-generated explanations that are meaningful to humans. Using the concept of weight of evidence from information theory, we develop a method for producing explanations that adhere to these principles. We show that this method can be adapted to handle high-dimensional, multi-class settings, yielding a flexible meta-algorithm for generating explanations. We demonstrate that these explanations can be estimated accurately from finite samples and are robust to small perturbations of the inputs. We also evaluate our method through a qualitative user study with machine learning practitioners, where we observe that the resulting explanations are usable despite some participants struggling with background concepts like prior class probabilities. Finally, we conclude by surfacing design implications for interpretability tools