Ishaq Aden-Ali

I’m a masters student supervised by Dr. Hassan Ashtiani in the Department of Computing and Software, McMaster University. I recently completed my undergraduate degree in Electrical Engineering at the same University. My name is pronounced Is-hak.

Research Interests:

I am mainly interested in studying problems at the intersection of theoretical computer science, machine learning and statistics. My current research focuses on questions related to statistical learning theory and distribution learning. In particular, I’m interested in understanding which problems can (or cannot!) be provably solved by algorithms that are both statistically and computationally efficient.

I am also very interested in private data analysis (via differential privacy) and mathematical optimization.

News

Dec 21, 2020	Our paper on privately learning high-dimensional Gaussians with Hassan and Gautam was accepted to ALT 2021.
Aug 26, 2020	I (virtually) presented our paper at AISTATS 2020.
Jan 6, 2020	Our paper “On the Sample Complexity of Learning Sum-Product Networks” with Hassan was accepted to AISTATS 2020.

Selected publications

ALT

On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians

Aden-Ali, I., Ashtiani, H., and Kamath, G.

International Conference on Algorithmic Learning Theory, 2020

Abs arXiv

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose restrictions on the parameters of the distribution. Our bounds are near-optimal in the case when the covariance is known to be the identity, and conjectured to be near-optimal in the general case. From a technical standpoint, we provide analytic tools for arguing the existence of global “locally small” covers from local covers of the space. These are exploited using modifications of recent techniques for differentially private hypothesis selection. Our techniques may prove useful for privately learning other distribution classes which do not possess a finite cover.
AISTATS

On the Sample Complexity of Learning Sum-Product Networks

Aden-Ali, I., and Ashtiani, H.

International Conference on Artificial Intelligence and Statistics, 2020

Abs arXiv

Sum-Product Networks (SPNs) can be regarded as a form of deep graphical models that compactly represent deeply factored and mixed distributions. An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their children distributions) and a set of product nodes (representing the products of its children distributions). In this work, we initiate the study of the sample complexity of PAC-learning the set of distributions that correspond to SPNs. We show that the sample complexity of learning tree structured SPNs with the usual type of leaves (i.e., Gaussian or discrete) grows at most linearly (up to logarithmic factors) with the number of parameters of the SPN. More specifically, we show that the class of distributions that corresponds to tree structured Gaussian SPNs with k mixing weights and e (d-dimensional Gaussian) leaves can be learned within Total Variation error ε using at most Õ((ed²+k)/ε²) samples. A similar result holds for tree structured SPNs with discrete leaves. We obtain the upper bounds based on the recently proposed notion of distribution compression schemes. More specifically, we show that if a (base) class of distributions ℱ admits an "efficient" compression, then the class of tree structured SPNs with leaves from ℱ also admits an efficient compression.