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Mark Davenport

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7 papers

1 author row

NeurIPS Conference 2023 Conference Paper

Perceptual adjustment queries and an inverted measurement paradigm for low-rank metric learning

Austin Xu
Andrew McRae
Jingyan Wang
Mark Davenport
Ashwin Pananjady

We introduce a new type of query mechanism for collecting human feedback, called the perceptual adjustment query (PAQ). Being both informative and cognitively lightweight, the PAQ adopts an inverted measurement scheme, and combines advantages from both cardinal and ordinal queries. We showcase the PAQ in the metric learning problem, where we collect PAQ measurements to learn an unknown Mahalanobis distance. This gives rise to a high-dimensional, low-rank matrix estimation problem to which standard matrix estimators cannot be applied. Consequently, we develop a two-stage estimator for metric learning from PAQs, and provide sample complexity guarantees for this estimator. We present numerical simulations demonstrating the performance of the estimator and its notable properties.

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NeurIPS Conference 2021 Conference Paper

Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through time

Feng Zhu
Andrew Sedler
Harrison A Grier
Nauman Ahad
Mark Davenport
Matthew Kaufman
Andrea Giovannucci
Chethan Pandarinath

Modern neural interfaces allow access to the activity of up to a million neurons within brain circuits. However, bandwidth limits often create a trade-off between greater spatial sampling (more channels or pixels) and the temporal frequency of sampling. Here we demonstrate that it is possible to obtain spatio-temporal super-resolution in neuronal time series by exploiting relationships among neurons, embedded in latent low-dimensional population dynamics. Our novel neural network training strategy, selective backpropagation through time (SBTT), enables learning of deep generative models of latent dynamics from data in which the set of observed variables changes at each time step. The resulting models are able to infer activity for missing samples by combining observations with learned latent dynamics. We test SBTT applied to sequential autoencoders and demonstrate more efficient and higher-fidelity characterization of neural population dynamics in electrophysiological and calcium imaging data. In electrophysiology, SBTT enables accurate inference of neuronal population dynamics with lower interface bandwidths, providing an avenue to significant power savings for implanted neuroelectronic interfaces. In applications to two-photon calcium imaging, SBTT accurately uncovers high-frequency temporal structure underlying neural population activity, substantially outperforming the current state-of-the-art. Finally, we demonstrate that performance could be further improved by using limited, high-bandwidth sampling to pretrain dynamics models, and then using SBTT to adapt these models for sparsely-sampled data.

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NeurIPS Conference 2020 Conference Paper

Generative causal explanations of black-box classifiers

Matthew O'Shaughnessy
Gregory Canal
Marissa Connor
Christopher Rozell
Mark Davenport

We develop a method for generating causal post-hoc explanations of black-box classifiers based on a learned low-dimensional representation of the data. The explanation is causal in the sense that changing learned latent factors produces a change in the classifier output statistics. To construct these explanations, we design a learning framework that leverages a generative model and information-theoretic measures of causal influence. Our objective function encourages both the generative model to faithfully represent the data distribution and the latent factors to have a large causal influence on the classifier output. Our method learns both global and local explanations, is compatible with any classifier that admits class probabilities and a gradient, and does not require labeled attributes or knowledge of causal structure. Using carefully controlled test cases, we provide intuition that illuminates the function of our causal objective. We then demonstrate the practical utility of our method on image recognition tasks.

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NeurIPS Conference 2020 Conference Paper

Sample complexity and effective dimension for regression on manifolds

Andrew McRae
Justin Romberg
Mark Davenport

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various implicit and explicit dimensionality-reduction methods that exploit manifold structure. Our first key contribution is to establish a novel nonasymptotic version of the Weyl law from differential geometry. From this we are able to show that certain spaces of smooth functions on a manifold are effectively finite-dimensional, with a complexity that scales according to the manifold dimension rather than any ambient data dimension. Finally, we show that given (potentially noisy) function values taken uniformly at random over a manifold, a kernel regression estimator (derived from the spectral decomposition of the manifold) yields minimax-optimal error bounds that are controlled by the effective dimension.

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NeurIPS Conference 2020 Conference Paper

Simultaneous Preference and Metric Learning from Paired Comparisons

Austin Xu
Mark Davenport

A popular model of preference in the context of recommendation systems is the so-called ideal point model. In this model, a user is represented as a vector u together with a collection of items x 1. .. x N in a common low-dimensional space. The vector u represents the user's "ideal point, " or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between u and an item x j indicates a stronger preference for x j. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences. In this paper, we consider the problem of learning an ideal point representation of a user's preferences when the distance metric is an unknown Mahalanobis metric. Specifically, we present a novel approach to estimate the user's ideal point u and the Mahalanobis metric from paired comparisons of the form "item x i is preferred to item x j. '' This can be viewed as a special case of a more general metric learning problem where the location of some points are unknown a priori. We conduct extensive experiments on synthetic and real-world datasets to exhibit the effectiveness of our algorithm.

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NeurIPS Conference 2016 Conference Paper

Dynamic matrix recovery from incomplete observations under an exact low-rank constraint

Liangbei Xu
Mark Davenport

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the {\em matrix sensing} and {\em matrix completion} observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.

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AAAI Conference 2015 Conference Paper

Active Manifold Learning via Gershgorin Circle Guided Sample Selection

Hongteng Xu
Hongyuan Zha
Ren-Cang Li
Mark Davenport

In this paper, we propose an interpretation of active learning from a pure algebraic view and combine it with semi-supervised manifold learning. The proposed active manifold learning algorithm aims to learn the lowdimensional parameter space of the manifold with high accuracy from smartly labeled samples. We demonstrate that this problem is equivalent to a condition number minimization problem of the alignment matrix. Focusing on this problem, we first give a theoretical upper bound for the solution. Then we develop a heuristic but effective sample selection algorithm with the help of the Gershgorin circle theorem. We investigate the rationality, the feasibility, the universality and the complexity of the proposed method and demonstrate that our method yields encouraging active learning results.

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