Summary: When using Markov chain Monte Carlo (MCMC) algorithms to perform inference for Bayesian clustering models, such as mixture models, the output is typically a sample of clusterings (partitions) drawn from the posterior distribution. In practice, a key challenge is how to summarise this output. Here we build upon the notion of the posterior similarity matrix (PSM) in order to suggest new approaches for summarising the output of MCMC algorithms for Bayesian clustering models. A key contribution of our work is the observation that PSMs are positive semi-definite, and hence can be used to define probabilistically-motivated kernel matrices that capture the clustering structure present in the data. This observation enables us to employ a range of kernel methods to obtain summary clusterings, and otherwise exploit the information summarised by PSMs. For example, if we have multiple PSMs, each corresponding to a different dataset on a common set of statistical units, we may use standard methods for combining kernels in order to perform integrative clustering. We may moreover embed PSMs within predictive kernel models in order to perform outcome-guided data integration. We demonstrate the performances of the proposed methods through a range of simulation studies as well as two real data applications.

Normalization techniques are essential for accelerating the training and improving the generalization of deep neural networks (DNNs), and have successfully been used in various applications. This paper reviews and comments on the past, present and future of normalization methods in the context of DNN training. We provide a unified picture of the main motivation behind different approaches from the perspective of optimization, and present a taxonomy for understanding the similarities and differences between them. Specifically, we decompose the pipeline of the most representative normalizing activation methods into three components: the normalization area partitioning, normalization operation and normalization representation recovery. In doing so, we provide insight for designing new normalization technique. Finally, we discuss the current progress in understanding normalization methods, and provide a comprehensive review of the applications of normalization for particular tasks, in which it can effectively solve the key issues.

This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model. This is useful when we are interested in jointly learning the causal effects of interventions on different subsets of variables in a DAG, which is common in field such as healthcare or operations research. We propose the first multi-task causal Gaussian process (GP) model, which we call DAG-GP, that allows for information sharing across continuous interventions and across experiments on different variables. DAG-GP accommodates different assumptions in terms of data availability and captures the correlation between functions lying in input spaces of different dimensionality via a well-defined integral operator. We give theoretical results detailing when and how the DAG-GP model can be formulated depending on the DAG. We test both the quality of its predictions and its calibrated uncertainties. Compared to single-task models, DAG-GP achieves the best fitting performance in a variety of real and synthetic settings. In addition, it helps to select optimal interventions faster than competing approaches when used within sequential decision making frameworks, like active learning or Bayesian optimization.

The impressive performance exhibited by modern machine learning models hinges on the ability to train such models on a very large amounts of labeled data. However, since access to large volumes of labeled data is often limited or expensive, it is desirable to alleviate this bottleneck by carefully curating the training set. Optimal experimental design is a well-established paradigm for selecting data point to be labeled so to maximally inform the learning process. Unfortunately, classical theory on optimal experimental design focuses on selecting examples in order to learn underparameterized (and thus, non-interpolative) models, while modern machine learning models such as deep neural networks are overparameterized, and oftentimes are trained to be interpolative. As such, classical experimental design methods are not applicable in many modern learning setups. Indeed, the predictive performance of underparameterized models tends to be variance dominated, so classical experimental design focuses on variance reduction, while the predictive performance of overparameterized models can also be, as is shown in this paper, bias dominated or of mixed nature. In this paper we propose a design strategy that is well suited for overparameterized regression and interpolation, and we demonstrate the applicability of our method in the context of deep learning by proposing a new algorithm for single-shot deep active learning.

We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information about the targets, in a decoder-agnostic fashion. In machine learning, however, our goal is not compression but rather generalization, which is intimately linked to the predictive family or decoder of interest (e.g. linear classifier). We propose the Decodable Information Bottleneck (DIB) that considers information retention and compression from the perspective of the desired predictive family. As a result, DIB gives rise to representations that are optimal in terms of expected test performance and can be estimated with guarantees. Empirically, we show that the framework can be used to enforce a small generalization gap on downstream classifiers and to predict the generalization ability of neural networks.

In this study we present the RENT feature selection method for binary classification and regression problems. We compare the performance of RENT to a number of other state-of-the-art feature selection methods on eight datasets (six for binary classification and two for regression) to illustrate RENT's performance with regard to prediction and reduction of total number of features. At its core RENT trains an ensemble of unique models using regularized elastic net to select features. Each model in the ensemble is trained with a unique and randomly selected subset from the full training data. From these models one can acquire weight distributions for each feature that contain rich information on the stability of feature selection and from which several adjustable classification criteria may be defined. Moreover, we acquire distributions of class predictions for each sample across many models in the ensemble. Analysis of these distributions may provide useful insight into which samples are more difficult to classify correctly than others. Overall, results from the tested datasets show that RENT not only can compete on-par with the best performing feature selection methods in this study, but also provides valuable insights into the stability of feature selection and sample classification.

Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When running the resulting prediction method on the training data or on test data, it can happen that an object is predicted to lie in a class that differs from its given label. This is sometimes called label bias, and raises the question whether the object was mislabeled. Our goal is to visualize aspects of the data classification to obtain insight. The proposed display reflects to what extent each object's label is (dis)similar to its prediction, how far each object lies from the other objects in its class, and whether some objects lie far from all classes. The display is constructed for discriminant analysis, the k-nearest neighbor classifier, support vector machines, logistic regression, and majority voting. It is illustrated on several benchmark datasets containing images and texts.

Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.

"Being good is easy, what is difficult is being just." "We need to defend the interests of those whom we've never met and never will." Note: This article is intended for a general audience to try and elucidate the complicated nature of unfairness in machine learning algorithms. As such, I have tried to explain concepts in an accessible way with minimal use of mathematics, in the hope that everyone can get something out of reading this. Supervised machine learning algorithms are inherently discriminatory. They are discriminatory in the sense that they use information embedded in the features of data to separate instances into distinct categories -- indeed, this is their designated purpose in life. This is reflected in the name for these algorithms which are often referred to as discriminative algorithms (splitting data into categories), in contrast to generative algorithms (generating data from a given category). When we use supervised machine learning, this "discrimination" is used as an aid to help us categorize our data into distinct categories within the data distribution, as illustrated below. Whilst this occurs when we apply discriminative algorithms -- such as support vector machines, forms of parametric regression (e.g.

Simple Linear regression is a simple yet powerful supervised learning technique. The aim of linear regression is to identify how the input variable(explanatory variable) influences the output variable(response variable). Simple Linear regression performs the task to predict a dependent variable value (y) based on a given independent variable (x). So, this regression technique finds out a linear relationship between x (input) and y(output). Hence, the name is Linear Regression. In the figure above, X (input) is the work experience and Y (output) is the salary of a person.