arXiv subjects

Ashia Wilson

Publications and source records attributed to Ashia Wilson.

29 records · Page 2Linked to original sources

arXiv2024

Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithm

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced by a single step of the Mirror Langevin algorithm (Zhang et al., 2020), which is a basic discretisation of the Mirror Langevin dynamics. Due to the inclusion of this filter, our method is unbiased relative to the target, while known discretisations of the Mirror Langevin dynamics including the Mirror Langevin algorithm have an asymptotic bias. For this algorithm, we also give upper bounds for the number of iterations taken to mix to a constrained distribution whose potential is relatively smooth, convex, and Lipschitz continuous with respect to a self-concordant mirror function. As a consequence of the reversibility of the Markov chain induced by the inclusion of the Metropolis-Hastings filter, we obtain an exponentially better dependence on the error tolerance for approximate constrained sampling. We also present numerical experiments that corroborate our theoretical findings.

stat.CO↗

arXiv2024

Scarce Resource Allocations That Rely On Machine Learning Should Be Randomized

Contrary to traditional deterministic notions of algorithmic fairness, this paper argues that fairly allocating scarce resources using machine learning often requires randomness. We address why, when, and how to randomize by proposing stochastic procedures that more adequately account for all of the claims that individuals have to allocations of social goods or opportunities.

cs.CY↗

arXiv2024

Algorithmic Pluralism: A Structural Approach To Equal Opportunity

We present a structural approach toward achieving equal opportunity in systems of algorithmic decision-making called algorithmic pluralism. Algorithmic pluralism describes a state of affairs in which no set of algorithms severely limits access to opportunity, allowing individuals the freedom to pursue a diverse range of life paths. To argue for algorithmic pluralism, we adopt Joseph Fishkin's theory of bottlenecks, which focuses on the structure of decision-points that determine how opportunities are allocated. The theory contends that each decision-point or bottleneck limits access to opportunities with some degree of severity and legitimacy. We extend Fishkin's structural viewpoint and use it to reframe existing systemic concerns about equal opportunity in algorithmic decision-making, such as patterned inequality and algorithmic monoculture. In proposing algorithmic pluralism, we argue for the urgent priority of alleviating severe bottlenecks in algorithmic decision-making. We contend that there must be a pluralism of opportunity available to many different individuals in order to promote equal opportunity in a systemic way. We further show how this framework has several implications for system design and regulation through current debates about equal opportunity in algorithmic hiring.

cs.CY↗

arXiv2024

Mean-field underdamped Langevin dynamics and its spacetime discretization

We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.

stat.CO↗

arXiv2024

DiffusionWorldViewer: Exposing and Broadening the Worldview Reflected by Generative Text-to-Image Models

Generative text-to-image (TTI) models produce high-quality images from short textual descriptions and are widely used in academic and creative domains. Like humans, TTI models have a worldview, a conception of the world learned from their training data and task that influences the images they generate for a given prompt. However, the worldviews of TTI models are often hidden from users, making it challenging for users to build intuition about TTI outputs, and they are often misaligned with users' worldviews, resulting in output images that do not match user expectations. In response, we introduce DiffusionWorldViewer, an interactive interface that exposes a TTI model's worldview across output demographics and provides editing tools for aligning output images with user perspectives. In a user study with 18 diverse TTI users, we find that DiffusionWorldViewer helps users represent their varied viewpoints in generated images and challenge the limited worldview reflected in current TTI models.

cs.LG↗

arXiv2023

Accelerated Stochastic Optimization Methods under Quasar-convexity

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.

math.OC↗

arXiv2022

Sufficient conditions for non-asymptotic convergence of Riemannian optimisation methods

Motivated by energy based analyses for descent methods in the Euclidean setting, we investigate a generalisation of such analyses for descent methods over Riemannian manifolds. In doing so, we find that it is possible to derive curvature-free guarantees for such descent methods. This also enables us to give the first known guarantees for a Riemannian cubic-regularised Newton algorithm over $g$-convex functions, which extends the guarantees by Agarwal et al [2021] for an adaptive Riemannian cubic-regularised Newton algorithm over general non-convex functions. This analysis leads us to study acceleration of Riemannian gradient descent in the $g$-convex setting, and we improve on an existing result by Alimisis et al [2021], albeit with a curvature-dependent rate. Finally, extending the analysis by Ahn and Sra [2020], we attempt to provide some sufficient conditions for the acceleration of Riemannian descent methods in the strongly geodesically convex setting.

math.OC↗

arXiv2022

Multilevel Optimization for Inverse Problems

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying framework of multilevel optimization that can be applied to a wide range of optimization-based solvers. Our framework provably reduces the computational cost associated with evaluating the expensive forward maps stemming from various physical models. To demonstrate the versatility of our analysis, we discuss its implications for various methodologies including multilevel (accelerated, stochastic) gradient descent, a multilevel ensemble Kalman inversion and a multilevel Langevin sampler. We also provide numerical experiments to verify our theoretical findings.

math.OC↗

arXiv2020

Approximate Cross-validation: Guarantees for Model Assessment and Selection

Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets. Recent work in empirical risk minimization (ERM) approximates the expensive refitting with a single Newton step warm-started from the full training set optimizer. While this can greatly reduce runtime, several open questions remain including whether these approximations lead to faithful model selection and whether they are suitable for non-smooth objectives. We address these questions with three main contributions: (i) we provide uniform non-asymptotic, deterministic model assessment guarantees for approximate CV; (ii) we show that (roughly) the same conditions also guarantee model selection performance comparable to CV; (iii) we provide a proximal Newton extension of the approximate CV framework for non-smooth prediction problems and develop improved assessment guarantees for problems such as l1-regularized ERM.

stat.ML↗

arXiv2020

Accelerating Rescaled Gradient Descent: Fast Optimization of Smooth Functions

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is strongly smooth -- a natural generalization of the standard smoothness assumption on the objective function. When the objective function is convex, we present two novel frameworks for "accelerating" descent methods, one in the style of Nesterov and the other in the style of Monteiro and Svaiter, using a single Lyapunov. Rescaled gradient descent can be accelerated under the same strong smoothness assumption using both frameworks. We provide several examples of strongly smooth loss functions in machine learning and numerical experiments that verify our theoretical findings. We also present several extensions of our novel Lyapunov framework, including deriving optimal universal tensor methods and extending our framework to the coordinate setting.

math.OC↗

arXiv2019

The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally

The long-term impact of algorithmic decision making is shaped by the dynamics between the deployed decision rule and individuals' response. Focusing on settings where each individual desires a positive classification---including many important applications such as hiring and school admissions, we study a dynamic learning setting where individuals invest in a positive outcome based on their group's expected gain and the decision rule is updated to maximize institutional benefit. By characterizing the equilibria of these dynamics, we show that natural challenges to desirable long-term outcomes arise due to heterogeneity across groups and the lack of realizability. We consider two interventions, decoupling the decision rule by group and subsidizing the cost of investment. We show that decoupling achieves optimal outcomes in the realizable case but has discrepant effects that may depend on the initial conditions otherwise. In contrast, subsidizing the cost of investment is shown to create better equilibria for the disadvantaged group even in the absence of realizability.

cs.GT↗