Related papers: Necessary and sufficient conditions for identifiab…
The principle of the identity of indiscernibles (PII) states that if two systems are qualitatively identical then they are logically identical. French and Redhead (1988) and Butterfield (1993) have shown the sense in which bosons and…
This paper deals with dynamic networks in which the causality relations between the vertex signals are represented by linear time-invariant transfer functions (modules). Considering an acyclic network where only a subset of its vertices are…
We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional mixtures of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental in performing necessary computations for, e.g., taking the…
1. Accurate estimates of demographic parameters are required to infer appropriate ecological relationships and inform management actions. Recently developed N-mixture models use count data from unmarked individuals to estimate demographic…
Latent class models with covariates are widely used for psychological, social, and educational research. Yet the fundamental identifiability issue of these models has not been fully addressed. Among the previous research on the…
Galactic chemical abundances provide crucial insights into fundamental galactic parameters, such as the high-mass slope of the initial mass function (IMF) and the normalization of Type Ia supernova (SN Ia) rates. Constraining these…
Polytopic matrix factorization (PMF) is a recently introduced matrix decomposition method in which the data vectors are modeled as linear transformations of samples from a polytope. The successful recovery of the original factors in the…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…
The present paper considers extremal combinatorics questions in the language of matrices. An $s$-matrix is a matrix with entries in $\{0,1,\ldots, s-1\}$. An $s$-matrix is simple if it has no repeated columns. A matrix $F$ is a…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
We present updated stellar population models appropriate for old ages (>1 Gyr) and covering a wide range in metallicities (-1.5<[Fe/H]<0.3). These models predict the full spectral variation associated with individual element abundance…
We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
We prove a low characteristic counterpart to the main result in (Peluse, 2019), establishing power saving bounds for the polynomial Szemer\'{e}di theorem for certain families of polynomials. Namely, we show that if $P_1, \dots, P_m \in…
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances…
For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…
Not all people are equally easy to identify: color statistics might be enough for some cases while others might require careful reasoning about high- and low-level details. However, prevailing person re-identification(re-ID) methods use…