Related papers: A Maximum Entropy Approach to Defining Cell State
The entropy of an electronic system offers important insights into the nature of its quantum mechanical ground state. This is particularly valuable in cases where the state is difficult to identify by conventional experimental probes, such…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
The method of optimizing entropy is used to (i) conduct Asymptotic Hypothesis Testing and (ii) determine the particle distribution for which Entropy is maximized. This paper focuses on two related applications of Information Theory:…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
We introduce a constructive framework for assigning thermodynamic structure to an arbitrary data system from its measured microstates. Starting from an empirical distribution over configurations, we first infer a data-driven energy function…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
Modern studies of societal phenomena rely on the availability of large datasets capturing attributes and activities of synthetic, city-level, populations. For instance, in epidemiology, synthetic population datasets are necessary to study…
To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the…
Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive,…
Single-cell RNA-seq data are challenging because of the sparseness of the read counts, the tiny expression of many relevant genes, and the variability in the efficiency of RNA extraction for different cells. We consider a simple…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…