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E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is…

In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…

The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. ID3,…

Focusing on the most significant features of a dataset is useful both in machine learning (ML) and data mining. In ML, it can lead to a higher accuracy, a faster learning process, and ultimately a simpler and more understandable model. In…

Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in…

Many real-world systems can be studied in terms of pattern recognition tasks, so that proper use (and understanding) of machine learning methods in practical applications becomes essential. While a myriad of classification methods have been…

A recent article proposed reduced mutual information for evaluation of clustering, classification and community detection. The motivation is that the standard normalized mutual information (NMI) may give counter-intuitive answers under…

The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…

We formulate an info-clustering paradigm based on a multivariate information measure, called multivariate mutual information, that naturally extends Shannon's mutual information between two random variables to the multivariate case…

In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically…

Using Arcminute Microkelvin Imager (AMI) SZ observations towards ten CLASH clusters we investigate the influence of cluster mergers on observational galaxy cluster studies. Although selected to be largely relaxed, there is disagreement in…

In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…

This report discusses two new indices for comparing clusterings of a set of points. The motivation for looking at new ways for comparing clusterings stems from the fact that the existing clustering indices are based on set cardinality alone…

Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…

Active clustering aims to boost the clustering performance by integrating human-annotated pairwise constraints through strategic querying. Conventional approaches with semi-supervised clustering schemes encounter high query costs when…

We propose Adaptive Incremental Mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric…

Normalized mutual information is widely used as a similarity measure for evaluating the performance of clustering and classification algorithms. In this paper, we argue that results returned by the normalized mutual information are biased…

Sample size determination for cluster randomised trials (CRTs) is challenging as it requires robust estimation of the intra-cluster correlation coefficient (ICC). Typically, the sample size is chosen to provide a certain level of power to…

Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…