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Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Multi-task learning is a method for improving the generalizability of multiple tasks. In order to perform multiple classification tasks with one neural network model, the losses of each task should be combined. Previous studies have mostly…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…
In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…
Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…
The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…
Feature selection is essential in the analysis of molecular systems and many other fields, but several uncertainties remain: What is the optimal number of features for a simplified, interpretable model that retains essential information?…
Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak…
Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a…
Voice Activity Detection (VAD) refers to the problem of distinguishing speech segments from background noise. Numerous approaches have been proposed for this purpose. Some are based on features derived from the power spectral density,…
Speech recognition and other natural language tasks have long benefited from voting-based algorithms as a method to aggregate outputs from several systems to achieve a higher accuracy than any of the individual systems. Diarization, the…
Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…
A wavelet-based changepoint method is proposed that determines when the variability of the noise in a sequence of functional profiles goes out-of-control from a known, fixed value. The functional portion of the profiles are allowed to come…
Detecting critical transitions in complex, noisy time-series data is a fundamental challenge across science and engineering. Such transitions may be anticipated by the emergence of a low-dimensional order parameter, whose signature is often…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We present a new approach for learning compact and intuitive distributed representations with binary encoding. Rather than summing up expert votes as in products of experts, we employ for each variable the opinion of the most reliable…