Related papers: Scaling Laws and Similarity Detection in Sequence …
Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…
We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$.…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Scaling laws have played a major role in the modern AI revolution, providing practitioners predictive power over how the model performance will improve with increasing data, compute, and number of model parameters. This has spurred an…
In the Correlation Clustering problem, we are given a weighted graph $G$ with its edges labeled as "similar" or "dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of "disagreements": the sum…
Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…
Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…
We propose a method for detecting differential gene expression that exploits the correlation between genes. Our proposal averages the univariate scores of each feature with the scores in correlation neighborhoods. In a number of real and…
Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single…
We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of…
A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension…
We derive the distribution of eigenvalues of the reduced density matrix of a block of length l in a one-dimensional system in the scaling regime. The resulting "entanglement spectrum" is described by a universal scaling function depending…
Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…
In this paper, we consider comparison-based adaptive stochastic algorithms for solving numerical optimisation problems. We consider a specific subclass of algorithms that we call comparison-based step-size adaptive randomized search…
We consider the `one-shot frame synchronization problem' where a decoder wants to locate a sync pattern at the output of a channel on the basis of sequential observations. We assume that the sync pattern of length N starts being emitted at…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
Neural visual decoding is a central problem in brain computer interface research, aiming to reconstruct human visual perception and to elucidate the structure of neural representations. However, existing approaches overlook a fundamental…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…