GRADUATE STUDENT SEMINAR, Information-preserving Dimensionality Reduction for High-dimensional Small-sample Data, Aditi Jha, Princeton University

Mon, Apr 17, 2023, 12:30 pm

Information-preserving Dimensionality Reduction for High-dimensional Small-sample Data

The analysis of high-dimensional data is an important challenge in machine learning, and in modern neuroscience. It is often desirable to reduce dimensionality while preserving information about some target variable of interest. For example, we may wish to identify the dimensions of a high-dimensional neural activity that carry information about a stimulus variable. This motivates sufficient dimension reduction (SDR) methods, which seek to identify a linear projection of high-dimensional data that preserves information about a target variable. However, existing methods typically require more observations than the data-dimensionality (N>p). High-throughput neural recordings often fall into the opposite regime, where we have fewer trials than the number of neurons (N<p). This renders existing SDR methods intractable, even though evidence suggests that neural activity varies meaningfully along only a small number of dimensions. Motivated by these, we propose Class-conditional Factor Analytic Dimensions (CFAD), a model-based dimensionality reduction method for high-dimensional, small-sample size data. The factor-analytic backbone of the model readily incorporates priors for known structure of the data, which we show improves performance in the small sample regime. We find that CFAD dramatically outperforms other methods in the small-sample high-imension regime, and demonstrate its effectiveness on functional magnetic resonance imaging (fMRI) measurements of brain activity during visual object recognition.

Aditi Jha is a fourth-year graduate student, jointly in the ECE and PNI. She is advised by Jonathan Pillow. Her primary research interests include developing machine learning methods to advance our understanding of decision-making and visual perception in humans and animals. Prior to joining Princeton, she studied Electrical Engineering as an undergraduate at Indian Institute of Technology, Delhi. She has also spent time doing research at Meta Reality Labs. Her research is generously supported by a Google PhD fellowship in computational neural and cognitive sciences.

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