Guillaume Rabusseau

farzaneh.heidari@mila.quebec

Beheshteh Toloueirakhshan

PhD - Université de Montréal

rakhshab@mila.quebec

Farzaneh Heidari

PhD - Université de Montréal

Co-supervisor :

Jian Tang

Julia Gastinger

Collaborating Alumni - University of Mannheim

Co-supervisor :

julia.gastinger@mila.quebec

Jun Dai

Postdoctorate - Université de Montréal

jun.dai@mila.quebec

marawan.gamal@mila.quebec

Marawan Gamal

PhD - Université de Montréal

michael.rizvi-martel@mila.quebec

Maude Lizaire

PhD - Université de Montréal

lizairem@mila.quebec

Michael Rizvi-Martel

Master's Research - Université de Montréal

Website

Shirzadkhani Razieh Shirzadkhani

Omar Chikar

Master's Research - Université de Montréal

omar.chikhar@mila.quebec

Collaborating researcher

Co-supervisor :

razieh.shirzadkhani@mila.quebec

Shenyang Huang

PhD - McGill University

Principal supervisor :

Master's Research - McGill University

Principal supervisor :

soroush.omranpour@mila.quebec

Publications

Lower and Upper Bounds on the Pseudo-Dimension of Tensor Network Models

Behnoush Khavari

Tensor network (TN) methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the mac… (see more)hine learning community for their ability to compactly represent very high-dimensional objects. TN methods can for example be used to efﬁciently learn linear models in exponentially large feature spaces [56]. In this work, we derive upper and lower bounds on the VC-dimension and pseudo-dimension of a large class of TN models for classiﬁcation, regression and completion. Our upper bounds hold for linear models parameterized by arbitrary TN structures, and we derive lower bounds for common tensor decomposition models (CP, Tensor Train, Tensor Ring and Tucker) showing the tightness of our general upper bound. These results are used to derive a generalization bound which can be applied to classiﬁcation with low-rank matrices as well as linear classiﬁers based on any of the commonly used tensor decomposition models. As a corollary of our results, we obtain a bound on the VC-dimension of the matrix product state classiﬁer introduced in [56] as a function of the so-called bond dimension (i.e. tensor train rank), which answers an open problem listed by Cirac, Garre-Rubio and Pérez-García in [13].

openreview.net

Rademacher Random Projections with Tensor Networks

Beheshteh T. Rakhshan

Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimen… (see more)sion of very high-dimensional tensors. Following the work in [30], we consider a tensorized random projection relying on Tensor Train (TT) decomposition where each element of the core tensors is drawn from a Rademacher distribution. Our theoretical results reveal that the Gaussian low-rank tensor represented in compressed form in TT format in [30] can be replaced by a TT tensor with core elements drawn from a Rademacher distribution with the same embedding size. Experiments on synthetic data demonstrate that tensorized Rademacher RP can outperform the tensorized Gaussian RP studied in [30]. In addition, we show both theoretically and experimentally, that the tensorized RP in the Matrix Product Operator (MPO) format is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projection map

2021-10-26

ArXiv (preprint)

Extracting Weighted Automata for Approximate Minimization in Language Modelling

Clara Lacroce

Prakash Panangaden

2021-08-25

Proceedings of the Fifteenth International Conference on Grammatical Inference (published)

proceedings.mlr.press

Understanding Capacity Saturation in Incremental Learning

Shenyang Huang

Vincent Francois-Lavet

2021-06-08

Canadian Conference on AI (published)

doi.org

Quantum Tensor Networks, Stochastic Processes, and Weighted Automata

Sandesh M. Adhikary

Siddarth Srinivasan

Jacob Miller

Byron Boots

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix prod… (see more)uct states, a tensor-train decomposition for probabilistic modeling, motivated by the need to tractably model many-body systems. But similar models have also been studied in the stochastic processes and weighted automata literature, with little work on how these bodies of work relate to each other. We address this gap by showing how stationary or uniform versions of popular quantum tensor network models have equivalent representations in the stochastic processes and weighted automata literature, in the limit of infinitely long sequences. We demonstrate several equivalence results between models used in these three communities: (i) uniform variants of matrix product states, Born machines and locally purified states from the quantum tensor networks literature, (ii) predictive state representations, hidden Markov models, norm-observable operator models and hidden quantum Markov models from the stochastic process literature,and (iii) stochastic weighted automata, probabilistic automata and quadratic automata from the formal languages literature. Such connections may open the door for results and methods developed in one area to be applied in another.

2021-03-18

Proceedings of The 24th International Conference on Artificial Intelligence and Statistics (published)

proceedings.mlr.press

Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata

Borja Balle

Clara Lacroce

Prakash Panangaden

Doina Precup

We address the approximate minimization problem for weighted finite automata (WFAs) with weights in …

2021-02-13

ArXiv (preprint)

doi.org

Assessing the Impact: Does an Improvement to a Revenue Management System Lead to an Improved Revenue?

Greta Laage

Emma Frejinger

Andrea Lodi

2021-01-13

ArXiv (preprint)

Estimating the Impact of an Improvement to a Revenue Management System: An Airline Application

Greta Laage

Emma Frejinger

William Hamilton

Andrea Lodi

Airlines have been making use of highly complex Revenue Management Systems to maximize revenue for decades. Estimating the impact of changin… (see more)g one component of those systems on an important outcome such as revenue is crucial, yet very challenging. It is indeed the difference between the generated value and the value that would have been generated keeping business as usual, which is not observable. We provide a comprehensive overview of counterfactual prediction models and use them in an extensive computational study based on data from Air Canada to estimate such impact. We focus on predicting the counterfactual revenue and compare it to the observed revenue subject to the impact. Our microeconomic application and small expected treatment impact stand out from the usual synthetic control applications. We present accurate linear and deep-learning counterfactual prediction models which achieve respectively 1.1% and 1% of error and allow to estimate a simulated effect quite accurately.

2021-01-01

arXiv.org (preprint)

dblp.uni-trier.de

Scalable Change Point Detection for Dynamic Graphs

Shenyang Huang

Real world networks often evolve in complex ways over time. Understanding anomalies in dynamic networks is crucial for applications such as … (see more)traffic accident detection, intrusion identification and detection of ecosystem disturbances. In this work, we focus on the problem of change point detection in dynamic graphs. The goal is to identify time steps where the graph structure deviates significantly from the norm. Despite empirical success of recent methods, building a change point detection method for real world dynamic graphs, which often scale to millions of nodes, remains an open question. To fill this gap, we propose LADdos, a scalable method for change point detection in dynamic graphs. LADdos brings together ideas from two recent works: an accurate change point detection method for graphs called LAD [10] which detects the changes in the full Laplacian spectrum of the graph in each timestamp, and the general framework of network density of states (DOS) [5] which models the distribution of the singular values through efficient approximation methods. In experiments with two common graph models –the Stochastic Block Model (SBM) and the Barabási-Albert (BA) model – we show that LADdos has equal performance to LAD, which is the current state-of-the-art, while being orders of magnitude faster. For instance, on a dynamic graph with total 21 million edges over 150 timestamps, LADdos achieves 100x speedup when compared to LAD.

2021-01-01

(published)

www.semanticscholar.org

A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix

Thang Doan

Mehdi Abbana Bennani

Bogdan Mazoure

Pierre Alquier

2021-01-01

AISTATS (published)

proceedings.mlr.press

Towards a Trace-Preserving Tensor Network Representation of Quantum Channels

Siddarth Srinivasan

Sandesh M. Adhikary

Jacob Miller

Bibek Pokharel

Byron Boots

The problem of characterizing quantum channels arises in a number of contexts such as quantum process tomography and quantum error correctio… (see more)n. However, direct approaches to parameterizing and optimizing the Choi matrix representation of quantum channels face a curse of dimensionality: the number of parameters scales exponentially in the number of qubits. Recently, Torlai et al. [2020] proposed using locally puriﬁed density operators (LPDOs), a tensor network representation of Choi matrices, to overcome the unfavourable scaling in parameters. While the LPDO structure allows it to satisfy a ‘complete positivity’ (CP) constraint required of physically valid quantum channels, it makes no guarantees about a similarly required ‘trace preservation’ (TP) constraint. In practice, the TP constraint is violated, and the learned quantum channel may even be trace-increasing, which is non-physical. In this work, we present the problem of optimizing over TP LPDOs, discuss two approaches to characterizing the TP constraints on LPDOs, and outline the next steps for developing an optimization scheme.

2021-01-01

(published)

www.semanticscholar.org

Horizontal gene transfer and recombination analysis of SARS-CoV-2 genes helps discover its close relatives and shed light on its origin

Vladimir Makarenkov

Bogdan Mazoure