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This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…
In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…
Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…
Prototypical examples that best summarizes and compactly represents an underlying complex data distribution communicate meaningful insights to humans in domains where simple explanations are hard to extract. In this paper we present…
The rapid advancement of data science and artificial intelligence has affected physics in numerous ways, including the application of Bayesian inference, setting the stage for a revolution in research methodology. Our group has proposed…
The funnel plot is a graphical visualisation of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modelling assumptions. Although perhaps not widely appreciated, a simple extension…
The amount of information available in spectro-polarimetric data is estimated. To this end, the intrinsic dimensionality of the data is inferred with the aid of a recently derived estimator based on nearest-neighbor considerations and…
Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a…
This paper develops a new mathematical framework for denoising in blind two-dimensional (2D) super-resolution upon using the atomic norm. The framework denoises a signal that consists of a weighted sum of an unknown number of time-delayed…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…
Modeling time series data remains a pervasive issue as the temporal dimension is inherent to numerous domains. Despite significant strides in time series forecasting, high noise-to-signal ratio, non-normality, non-stationarity, and lack of…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…