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We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the…

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…

Motivation: A major challenge in the development of machine learning based methods in computational biology is that data may not be accurately labeled due to the time and resources required for experimentally annotating properties of…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…

Variational approaches to disparity estimation typically use a linearised brightness constancy constraint, which only applies in smooth regions and over small distances. Accordingly, current variational approaches rely on a schedule to…

We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that…

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

Predictive Coding Networks (PCNs) aim to learn a generative model of the world. Given observations, this generative model can then be inverted to infer the causes of those observations. However, when training PCNs, a noticeable pathology is…

Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…

The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…

The conformational landscape of proteins is crucial to understanding their functionality in complex biological processes. Traditional physics-based computational methods, such as molecular dynamics (MD) simulations, suffer from rare event…

In this work, we propose a novel centrality metric, referred to as star centrality, which incorporates information from the closed neighborhood of a node, rather than solely from the node itself, when calculating its topological importance.…

Protein language models are increasingly used to guide experimental and clinical decisions, yet it is often unclear whether a confident prediction reflects recognition of biological evidence or retrieval of a statistical default. We examine…

Feedback alignment algorithms are an alternative to backpropagation to train neural networks, whereby some of the partial derivatives that are required to compute the gradient are replaced by random terms. This essentially transforms the…

The generation of protein crystals is necessary for the study of protein molecular function and structure. This is done empirically by processing large numbers of crystallization trials and inspecting them regularly in search of those with…

Discerning how a mutation affects the stability of a protein is central to the study of a wide range of diseases. Machine learning and statistical analysis techniques can inform how to allocate limited resources to the considerable time and…