Related papers: A Tutorial on Multivariate $k$-Statistics and thei…
Economic policy and research rely on the correct evaluation of the billions of high-frequency data points that we collect every day. Consistent clustering algorithms, like DBSCAN, allow us to make sense of the data in a useful way. However,…
The basic goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript we focus on the analysis of non-Gaussian distributed data. In the…
Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…
When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…
$k$-subset sampling is ubiquitous in machine learning, enabling regularization and interpretability through sparsity. The challenge lies in rendering $k$-subset sampling amenable to end-to-end learning. This has typically involved relaxing…
In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…
Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most…
The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or…
In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting…
The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…
Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…
This paper introduces a new approach for Multivariate Time Series forecasting that jointly infers and leverages relations among time series. Its modularity allows it to be integrated with current univariate methods. Our approach allows to…
In this paper we present the development of a modulated web based statistical system, hereafter MWStat, which shifts the statistical paradigm of analyzing data into a real time structure. The MWStat system is useful for both online storage…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…
Comparative meta-analyses of groups of subjects by integrating multiple observational studies rely on estimated propensity scores (PSs) to mitigate covariate imbalances. However, PS estimation grapples with the theoretical and practical…
By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way…