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We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…
Network data often represent multiple types of relations, which can also denote exchanged quantities, and are typically encompassed in a weighted multiplex. Such data frequently exhibit clustering structures, however, traditional clustering…
The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex…
We present a novel compression algorithm for reducing the storage of LiDAR sensor data streams. Our model exploits spatio-temporal relationships across multiple LiDAR sweeps to reduce the bitrate of both geometry and intensity values.…
Visual recognition algorithms are required today to exhibit adaptive abilities. Given a deep model trained on a specific, given task, it would be highly desirable to be able to adapt incrementally to new tasks, preserving scalability as the…
Under extreme operating conditions, characterized by high particle multiplicity and heavily overlapping shower energy deposits, classical particle flow algorithms encounter pronounced limitations in resolution, efficiency, and accuracy. To…
We show that for complex nonlinear systems, model reduction and compressive sensing strategies can be combined to great advantage for classifying, projecting, and reconstructing the relevant low-dimensional dynamics. $\ell_2$-based…
With the benefit of deep learning techniques, recent researches have made significant progress in image compression artifacts reduction. Despite their improved performances, prevailing methods only focus on learning a mapping from the…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
The doubly robust estimator, which models both the propensity score and outcomes, is a popular approach to estimate the average treatment effect in the potential outcome setting. The primary appeal of this estimator is its theoretical…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex…
In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising…
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…
Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…