In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.

In this study, we use persistent homology to perform classification tasks on two publicly available multivariate time series datasets [19, 11] that include physiological data collected during stressful and non stressful tasks. Instead of directly computing signal-specific features from sliding windows and subwindows on modalities such as electrocardiogram and wrist temperature (Figure 7), we extracted features using persistence diagrams and their statistical properties. Subwindowing method allowed us to reduce noise without incurring an extra computational cost. We then developed machine learning models and assess the performance of our models by varying window sizes and using different flavors of persistence diagrams. Topological Data Analysis (TDA) techniques usually work with points embedded in an affine space of large enough dimension. However, TDA techniques can still be applied to time series data sets whether they are univariate or multivariate. One can convert a univariate time series into a finite collection of points in a -dimensional affine space using delay embedding methods, of which one can compute persistent homology. Since Taken's Theorem implies that the delay embeddings produces topologically invariant subsets on a non-chaotical dynamical system [21], one can reasonably expect that persistent homology produces features that would distinguish different time series. There is a handful of research on the persistent homology of delay embeddings for time series classification [23, 20, 1].

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim, we propose a novel method that leverages on Hidden Markov Models and Gaussian Graphical Models -- Time Adaptive Gaussian Model (TAGM). Our model is a generalization of state-of-the-art methods for the inference of temporal graphical models, its formulation leverages on both aspects of these models providing better results than current methods. In particular,it performs pattern recognition by clustering data points in time; and, it finds probabilistic (and possibly causal) relationships among the observed variables. Compared to current methods for temporal network inference, it reduces the basic assumptions while still showing good inference performances.

The area of graph embeddings is currently dominated by contrastive learning methods, which demand formulation of an explicit objective function and sampling of positive and negative examples. This creates a conceptual and computational overhead. Simple, classic unsupervised approaches like Multidimensional Scaling (MSD) or the Laplacian eigenmap skip the necessity of tedious objective optimization, directly exploiting data geometry. Unfortunately, their reliance on very costly operations such as matrix eigendecomposition make them unable to scale to large graphs that are common in today's digital world. In this paper we present Cleora: an algorithm which gets the best of two worlds, being both unsupervised and highly scalable. We show that high quality embeddings can be produced without the popular step-wise learning framework with example sampling. An intuitive learning objective of our algorithm is that a node should be similar to its neighbors, without explicitly pushing disconnected nodes apart. The objective is achieved by iterative weighted averaging of node neigbors' embeddings, followed by normalization across dimensions. Thanks to the averaging operation the algorithm makes rapid strides across the embedding space and usually reaches optimal embeddings in just a few iterations. Cleora runs faster than other state-of-the-art CPU algorithms and produces embeddings of competitive quality as measured on downstream tasks: link prediction and node classification. We show that Cleora learns a data abstraction that is similar to contrastive methods, yet at much lower computational cost. We open-source Cleora under the MIT license allowing commercial use under https://github.com/Synerise/cleora.

Mathematical modelling of unemployment dynamics attempts to predict the probability of a job seeker finding a job as a function of time. This is typically achieved by using information in unemployment records. These records are right censored, making survival analysis a suitable approach for parameter estimation. The proposed model uses a deep artificial neural network (ANN) as a non-linear hazard function. Through embedding, high-cardinality categorical features are analysed efficiently. The posterior distribution of the ANN parameters are estimated using a variational Bayes method. The model is evaluated on a time-to-employment data set spanning from 2011 to 2020 provided by the Slovenian public employment service. It is used to determine the employment probability over time for each individual on the record. Similar models could be applied to other questions with multi-dimensional, high-cardinality categorical data including censored records. Such data is often encountered in personal records, for example in medical records.

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. The encouraging results combined with advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). We contribute to this development by presenting a probabilistic VFM based on a Bayesian neural network. We consider homoscedastic and heteroscedastic measurement noise, and show how to train the models using maximum a posteriori estimation and variational inference. We study the methods by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where we achieve an average error of 5-6% and 9-13% for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. The difference in prediction performance and uncertainty on historical and future data is explored in detail, and the findings motivate the development of alternative strategies for data-driven VFM.

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the input measures, which are not restricted to being discrete. While past approaches rely on entropic or quadratic regularization, we employ input convex neural networks and cycle-consistency regularization to avoid introducing bias. As a result, our approach does not resort to minimax optimization. We provide theoretical analysis on error bounds as well as empirical evidence of the effectiveness of the proposed approach in low-dimensional qualitative scenarios and high-dimensional quantitative experiments.

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a simple generalization of the adaptive interpolation method in Bayesian inference for linear regimes to sub-linear ones. A modification of the well-known approximate message passing algorithm to approach the MMSE fundamental limit is also proposed. Our results show that the traditional linear assumption between the signal dimension and number of observations in the replica and adaptive interpolation methods is not necessary for sparse signals. They also show how to modify the existing well-known AMP algorithms for linear regimes to sub-linear ones.

Artificial intelligence (AI) systems have become increasingly common and the trend will continue. Examples of AI systems include autonomous vehicles (AV), computer vision, natural language processing, and AI medical experts. To allow for safe and effective deployment of AI systems, the reliability of such systems needs to be assessed. Traditionally, reliability assessment is based on reliability test data and the subsequent statistical modeling and analysis. The availability of reliability data for AI systems, however, is limited because such data are typically sensitive and proprietary. The California Department of Motor Vehicles (DMV) oversees and regulates an AV testing program, in which many AV manufacturers are conducting AV road tests. Manufacturers participating in the program are required to report recurrent disengagement events to California DMV. This information is being made available to the public. In this paper, we use recurrent disengagement events as a representation of the reliability of the AI system in AV, and propose a statistical framework for modeling and analyzing the recurrent events data from AV driving tests. We use traditional parametric models in software reliability and propose a new nonparametric model based on monotonic splines to describe the event process. We develop inference procedures for selecting the best models, quantifying uncertainty, and testing heterogeneity in the event process. We then analyze the recurrent events data from four AV manufacturers, and make inferences on the reliability of the AI systems in AV. We also describe how the proposed analysis can be applied to assess the reliability of other AI systems.

This paper investigates the prospects of using directive explanations to assist people in achieving recourse of machine learning decisions. Directive explanations list which specific actions an individual needs to take to achieve their desired outcome. If a machine learning model makes a decision that is detrimental to an individual (e.g. denying a loan application), then it needs to both explain why it made that decision and also explain how the individual could obtain their desired outcome (if possible). At present, this is often done using counterfactual explanations, but such explanations generally do not tell individuals how to act. We assert that counterfactual explanations can be improved by explicitly providing people with actions they could use to achieve their desired goal. This paper makes two contributions. First, we present the results of an online study investigating people's perception of directive explanations. Second, we propose a conceptual model to generate such explanations. Our online study showed a significant preference for directive explanations ($p<0.001$). However, the participants' preferred explanation type was affected by multiple factors, such as individual preferences, social factors, and the feasibility of the directives. Our findings highlight the need for a human-centred and context-specific approach for creating directive explanations.