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High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
An exciting new algorithmic breakthrough has been advanced for how to carry out inferences in a Dempster-Shafer (DS) formulation of a categorical data generating model. The developed sampling mechanism, which draws on theory for directed…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…
The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from…
We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
Epidemiologists increasingly use causal inference methods that rely on machine learning, as these approaches can relax unnecessary model specification assumptions. While deriving and studying asymptotic properties of such estimators is a…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach employs structural causal models that postulate noisy functional relations among a set of interacting variables.…
We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat…
We use experiment-supported dimensional analysis to further bolster our arguments that crucial information on the emergence and/or nature of space could be extracted from the combination of the properties of gravitational and strong…
An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth.…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
Dimensionality effects pose major challenges in high-dimensional and non-Euclidean data analysis. Graph-based two-sample tests and change-point detection are particularly attractive in this context, as they make minimal distributional…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…