Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems where the prediction is categorical, such as accepting or rejecting a loan application. This is in part because classification fairness measures are easily computed by comparing the rates of outcomes, leading to behaviours such as ensuring that the same fraction of eligible men are selected as eligible women. But such measures are computationally difficult to generalise to the continuous regression setting for problems such as pricing, or allocating payments. The difficulty arises from estimating conditional densities (such as the probability density that a system will over-charge by a certain amount). For the regression setting we introduce tractable approximations of the independence, separation and sufficiency criteria by observing that they factorise as ratios of different conditional probabilities of the protected attributes. We introduce and train machine learning classifiers, distinct from the predictor, as a mechanism to estimate these probabilities from the data. This naturally leads to model agnostic, tractable approximations of the criteria, which we explore experimentally.

Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we also propose the so-called \emph{permutation test} for persistence diagrams to delineate critical values and pairings of critical values. For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests. Our results help provide insights on when persistence diagram based summaries could be more suitable.

We derive the optimal differential privacy (DP) parameters of a mechanism that satisfies a given level of R enyi differential privacy (RDP). Our result is based on the joint range of two f -divergences that underlie the approximate and the R enyi variations of differential privacy. We apply our result to the moments accountant framework for characterizing privacy guarantees of stochastic gradient descent. When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget. Differential privacy (DP) [1] has become the de facto standard for privacy-preserving data analytics. Intuitively, a (potentially randomized) algorithm is said to be differentially private if its output does not vary significantly with small perturbations of the input. DP guarantees are usually cast in terms of properties of the information density [2] of the output of the algorithm conditioned on a given input--referred to as the privacy loss variable in the DP literature.

This note discusses a simple modification of cross-conformal prediction inspired by recent work on e-values. The precursor of conformal prediction developed in the 1990s by Gammerman, Vapnik, and Vovk was also based on e-values and is called conformal e-prediction in this note. Replacing e-values by p-values led to conformal prediction, which has important advantages over conformal e-prediction without obvious disadvantages. The situation with cross-conformal prediction is, however, different: whereas for cross-conformal prediction validity is only an empirical fact (and can be broken with excessive randomization), this note draws the reader's attention to the obvious fact that cross-conformal e-prediction enjoys a guaranteed property of validity.

Accurate and reliable forecasting of total cloud cover (TCC) is vital for many areas such as astronomy, energy demand and production, or agriculture. Most meteorological centres issue ensemble forecasts of TCC, however, these forecasts are often uncalibrated and exhibit worse forecast skill than ensemble forecasts of other weather variables. Hence, some form of post-processing is strongly required to improve predictive performance. As TCC observations are usually reported on a discrete scale taking just nine different values called oktas, statistical calibration of TCC ensemble forecasts can be considered a classification problem with outputs given by the probabilities of the oktas. This is a classical area where machine learning methods are applied. We investigate the performance of post-processing using multilayer percep-tron (MLP) neural networks, gradient boosting machines (GBM) and random forest (RF) methods. Based on the European Centre for Medium-Range Weather Forecasts global TCC ensemble forecasts for 2002-2014 we compare these approaches with the proportional odds logistic regression (POLR) and multiclass logistic regression (MLR) models, as well as the raw TCC ensemble forecasts. We further assess whether improvements in forecast skill can be obtained by incorporating ensemble forecasts of precipitation as additional predictor. Compared to the raw ensemble, all calibration methods result in a significant improvement in forecast skill. RF models provide the smallest increase in predictive performance, while MLP, POLR and GBM approaches perform best. Key words: ensemble calibration; gradient boosting machine; logistic regression; mul-tilayer perceptron; random forest; total cloud cover 1 Introduction Reliable and accurate prediction of total cloud cover (TCC) has a principal importance in observational astronomy (Ye and Chen, 2013) and in the prediction of photovoltaic energy production, as it is the main cause of variation in solar-radiation energy supply (Matuszko, 2012; McEvoy et al., 2012), but it is also of great relevance in agriculture, tourism and in some other fields of economy.

The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. We use microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. We apply nuclear density functional theory with several energy density functionals. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. We characterize the drip-line regions where the probability that the nucleus is particle-bound decreases from $1$ to $0$. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\leq 119$ have a probability of existence $\geq 0.5$. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to train machine learning models in large-scale distributed shared-memory and message-passing environments. Many of these models are trained employing variants of stochastic gradient descent (SGD) based optimization. In this paper, we introduce a general consistency condition covering communication-reduced and asynchronous distributed SGD implementations. Our framework, called elastic consistency enables us to derive convergence bounds for a variety of distributed SGD methods used in practice to train large-scale machine learning models. The proposed framework de-clutters the implementation-specific convergence analysis and provides an abstraction to derive convergence bounds. We utilize the framework to analyze a sparsification scheme for distributed SGD methods in an asynchronous setting for convex and non-convex objectives. We implement the distributed SGD variant to train deep CNN models in an asynchronous shared-memory setting. Empirical results show that error-feedback may not necessarily help in improving the convergence of sparsified asynchronous distributed SGD, which corroborates an insight suggested by our convergence analysis.

We consider the effect of structure-agnostic and structure-dependent masking schemes when training a universal marginaliser (arXiv:1711.00695) in order to learn conditional distributions of the form $P(x_i |\mathbf x_{\mathbf b})$, where $x_i$ is a given random variable and $\mathbf x_{\mathbf b}$ is some arbitrary subset of all random variables of the generative model of interest. In other words, we mimic the self-supervised training of a denoising autoencoder, where a dataset of unlabelled data is used as partially observed input and the neural approximator is optimised to minimise reconstruction loss. We focus on studying the underlying process of the partially observed data---how good is the neural approximator at learning all conditional distributions when the observation process at prediction time differs from the masking process during training? We compare networks trained with different masking schemes in terms of their predictive performance and generalisation properties.

Big Data scenarios pose a new challenge to traditional data mining algorithms, since they are not prepared to work with such amount of data. Smart Data refers to data of enough quality to improve the outcome from a data mining algorithm. Existing data mining algorithms unability to handle Big Datasets prevents the transition from Big to Smart Data. Automation in data acquisition that characterizes Big Data also brings some problems, such as differences in data size per class. This will lead classifiers to lean towards the most represented classes. This problem is known as imbalanced data distribution, where one class is underrepresented in the dataset. Ensembles of classifiers are machine learning methods that improve the performance of a single base classifier by the combination of several of them. Ensembles are not exempt from the imbalanced classification problem. To deal with this issue, the ensemble method have to be designed specifically. In this paper, a data preprocessing ensemble for imbalanced Big Data classification is presented, with focus on two-class problems. Experiments carried out in 21 Big Datasets have proved that our ensemble classifier outperforms classic machine learning models with an added data balancing method, such as Random Forests.

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample efficiency, Bayesian Optimization over a Gaussian Processes modeling of the parameter space has become the method of choice. Unfortunately, this approach suffers from a cubic compute complexity due to underlying Cholesky factorization, which makes it very hard to be scaled beyond a small number of sampling steps. In this paper, we present a novel, highly accurate approximation of the underlying Gaussian Process. Reducing its computational complexity from cubic to quadratic allows an efficient strong scaling of Bayesian Optimization while outperforming the previous approach regarding optimization accuracy. The first experiments show speedups of a factor of 162 in single node and further speed up by a factor of 5 in a parallel environment.