To be able to produce accurate and reliable predictions of visibility has crucial importance in aviation meteorology, as well as in water- and road transportation. Nowadays, several meteorological services provide ensemble forecasts of visibility; however, the skill, and reliability of visibility predictions are far reduced compared to other variables, such as temperature or wind speed. Hence, some form of calibration is strongly advised, which usually means estimation of the predictive distribution of the weather quantity at hand either by parametric or non-parametric approaches, including also machine learning-based techniques. As visibility observations - according to the suggestion of the World Meteorological Organization - are usually reported in discrete values, the predictive distribution for this particular variable is a discrete probability law, hence calibration can be reduced to a classification problem. Based on visibility ensemble forecasts of the European Centre for Medium-Range Weather Forecasts covering two slightly overlapping domains in Central and Western Europe and two different time periods, we investigate the predictive performance of locally, semi-locally and regionally trained proportional odds logistic regression (POLR) and multilayer perceptron (MLP) neural network classifiers. We show that while climatological forecasts outperform the raw ensemble by a wide margin, post-processing results in further substantial improvement in forecast skill and in general, POLR models are superior to their MLP counterparts.

In domains with high stakes such as law, recruitment, and healthcare, learning models frequently rely on sensitive user data for inference, necessitating the complete set of features. This not only poses significant privacy risks for individuals but also demands substantial human effort from organizations to verify information accuracy. This paper asks whether it is necessary to use \emph{all} input features for accurate predictions at inference time. The paper demonstrates that, in a personalized setting, individuals may only need to disclose a small subset of their features without compromising decision-making accuracy. The paper also provides an efficient sequential algorithm to determine the appropriate attributes for each individual to provide. Evaluations across various learning tasks show that individuals can potentially report as little as 10\% of their information while maintaining the same accuracy level as a model that employs the full set of user information.

This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative probability functions. We then provide a library of examples of these functions and a system for composing them. Additionally, we discuss a relative version of Bayesian inference and its digital implementation. Finally, we prove the topological closure of the relative probability space, highlighting its ability to preserve information under limits.

Advances in neuroscience have enabled researchers to measure the activities of large numbers of neurons simultaneously in behaving animals. We have access to the fluorescence of each of the neurons which provides a first-order approximation of the neural activity over time. Determining the exact spike of a neuron from this fluorescence trace constitutes an active area of research within the field of computational neuroscience. We propose a novel Bayesian approach based on a mixture of half-non-local prior densities and point masses for this task. Instead of a computationally expensive MCMC algorithm, we adopt a stochastic search-based approach that is capable of taking advantage of modern computing environments often equipped with multiple processors, to explore all possible arrangements of spikes and lack thereof in an observed spike train. It then reports the highest posterior probability arrangement of spikes and posterior probability for a spike at each location of the spike train. Our proposals lead to substantial improvements over existing proposals based on L1 regularization, and enjoy comparable estimation accuracy to the state-of-the-art L0 proposal, in simulations, and on recent calcium imaging data sets. Notably, contrary to optimization-based frequentist approaches, our methodology yields automatic uncertainty quantification associated with the spike-train inference.

The advent of ML-driven decision-making and policy formation has led to an increasing focus on algorithmic fairness. As clustering is one of the most commonly used unsupervised machine learning approaches, there has naturally been a proliferation of literature on {\em fair clustering}. A popular notion of fairness in clustering mandates the clusters to be {\em balanced}, i.e., each level of a protected attribute must be approximately equally represented in each cluster. Building upon the original framework, this literature has rapidly expanded in various aspects. In this article, we offer a novel model-based formulation of fair clustering, complementing the existing literature which is almost exclusively based on optimizing appropriate objective functions.

In recent years, deep neural networks (DNNs) have achieved remarkable success in various tasks such as image recognition, natural language processing, and speech recognition. However, despite their excellent performance, these models have certain limitations, such as their lack of uncertainty quantification (UQ). Much of UQ for DNNs is based on a Bayesian approach that models network weights as random variables [22] or has involved ensembles of networks [18]. Gaussian processes (GPs) provide natural UQ, but they lack the representation learning that makes DNNs successful. Standard GPs are known to scale poorly with large datasets, but GP approximations are plentiful and one such method is the Vecchia approximation [31, 16], which uses nearest-neighbor conditioning sets to exploit conditional independence among the data.

We consider the finite sum minimization of $n$ strongly convex and smooth functions with Lipschitz continuous Hessians in $d$ dimensions. In many applications where such problems arise, including maximum likelihood estimation, empirical risk minimization, and unsupervised learning, the number of observations $n$ is large, and it becomes necessary to use incremental or stochastic algorithms whose per-iteration complexity is independent of $n$. Of these, the incremental/stochastic variants of the Newton method exhibit superlinear convergence, but incur a per-iteration complexity of $O(d^3)$, which may be prohibitive in large-scale settings. On the other hand, the incremental Quasi-Newton method incurs a per-iteration complexity of $O(d^2)$ but its superlinear convergence rate has only been characterized asymptotically. This work puts forth the Sharpened Lazy Incremental Quasi-Newton (SLIQN) method that achieves the best of both worlds: an explicit superlinear convergence rate with a per-iteration complexity of $O(d^2)$. Building upon the recently proposed Sharpened Quasi-Newton method, the proposed incremental variant incorporates a hybrid update strategy incorporating both classic and greedy BFGS updates. The proposed lazy update rule distributes the computational complexity between the iterations, so as to enable a per-iteration complexity of $O(d^2)$. Numerical tests demonstrate the superiority of SLIQN over all other incremental and stochastic Quasi-Newton variants.

This study presents our team PathToMyHeart's contribution to the George B. Moody PhysioNet Challenge 2022. Two models are implemented. The first model is a Dual Bayesian ResNet (DBRes), where each patient's recording is segmented into overlapping log mel spectrograms. These undergo two binary classifications: present versus unknown or absent, and unknown versus present or absent. The classifications are aggregated to give a patient's final classification. The second model is the output of DBRes integrated with demographic data and signal features using XGBoost.DBRes achieved our best weighted accuracy of $0.771$ on the hidden test set for murmur classification, which placed us fourth for the murmur task. (On the clinical outcome task, which we neglected, we scored 17th with costs of $12637$.) On our held-out subset of the training set, integrating the demographic data and signal features improved DBRes's accuracy from $0.762$ to $0.820$. However, this decreased DBRes's weighted accuracy from $0.780$ to $0.749$. Our results demonstrate that log mel spectrograms are an effective representation of heart sound recordings, Bayesian networks provide strong supervised classification performance, and treating the ternary classification as two binary classifications increases performance on the weighted accuracy.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Machine Learning and Deep Learning have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction, which is the primary strength of most supervised machine learning algorithms, the quantification of uncertainty is relevant and necessary as well. While first concepts and ideas in this direction have emerged in recent years, this paper adopts a conceptual perspective and examines possible sources of uncertainty. By adopting the viewpoint of a statistician, we discuss the concepts of aleatoric and epistemic uncertainty, which are more commonly associated with machine learning. The paper aims to formalize the two types of uncertainty and demonstrates that sources of uncertainty are miscellaneous and can not always be decomposed into aleatoric and epistemic. Drawing parallels between statistical concepts and uncertainty in machine learning, we also demonstrate the role of data and their influence on uncertainty.