InfoNCE Loss Provably Learns Cluster-Preserving Representations

The goal of contrasting learning is to learn a representation that preserves underlying clusters by keeping samples with similar content, e.g. the ``dogness'' of a dog, close to each other in the space generated by the representation. A common and successful approach for tackling this unsupervised learning problem is minimizing the InfoNCE loss associated with the training samples, where each sample is associated with their augmentations (positive samples such as rotation, crop) and a batch of negative samples (unrelated samples). To the best of our knowledge, it was unanswered if the representation learned by minimizing the InfoNCE loss preserves the underlying data clusters, as it only promotes learning a representation that is faithful to augmentations, i.e., an image and its augmentations have the same representation. Our main result is to show that the representation learned by InfoNCE with a finite number of negative samples is also consistent with respect to clusters in the data, under the condition that the augmentation sets within clusters may be non-overlapping but are close and intertwined, relative to the complexity of the learning function class.

Score-based Causal Representation Learning with Interventions

This paper studies causal representation learning problem when the latent causal variables are observed indirectly through an unknown linear transformation. The objectives are: (i) recovering the unknown linear transformation (up to scaling and ordering), and (ii) determining the directed acyclic graph (DAG) underlying the latent variables. Since identifiable representation learning is impossible based on only observational data, this paper uses both observational and interventional data. The interventional data is generated under distinct single-node randomized hard and soft interventions. These interventions are assumed to cover all nodes in the latent space. It is established that the latent DAG structure can be recovered under soft randomized interventions via the following two steps. First, a set of transformation candidates is formed by including all inverting transformations corresponding to which the \emph{score} function of the transformed variables has the minimal number of coordinates that change between an interventional and the observational environment summed over all pairs. Subsequently, this set is distilled using a simple constraint to recover the latent DAG structure. For the special case of hard randomized interventions, with an additional hypothesis testing step, one can also uniquely recover the linear transformation, up to scaling and a valid causal ordering. These results generalize the recent results that either assume deterministic hard interventions or linear causal relationships in the latent space.

Optimal Algorithms for Latent Bandits with Cluster Structure

We consider the problem of latent bandits with cluster structure where there are multiple users, each with an associated multi-armed bandit problem. These users are grouped into \emph{latent} clusters such that the mean reward vectors of users within the same cluster are identical. At each round, a user, selected uniformly at random, pulls an arm and observes a corresponding noisy reward. The goal of the users is to maximize their cumulative rewards. This problem is central to practical recommendation systems and has received wide attention of late \cite{gentile2014online, maillard2014latent}. Now, if each user acts independently, then they would have to explore each arm independently and a regret of $\Omega(\sqrt{\mathsf{MNT}})$ is unavoidable, where $\mathsf{M}, \mathsf{N}$ are the number of arms and users, respectively. Instead, we propose LATTICE (Latent bAndiTs via maTrIx ComplEtion) which allows exploitation of the latent cluster structure to provide the minimax optimal regret of $\widetilde{O}(\sqrt{(\mathsf{M}+\mathsf{N})\mathsf{T}})$, when the number of clusters is $\widetilde{O}(1)$. This is the first algorithm to guarantee such a strong regret bound. LATTICE is based on a careful exploitation of arm information within a cluster while simultaneously clustering users. Furthermore, it is computationally efficient and requires only $O(\log{\mathsf{T}})$ calls to an offline matrix completion oracle across all $\mathsf{T}$ rounds.

Causal Bandits for Linear Structural Equation Models

This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model to minimize the cumulative regret with respect to the best intervention in hindsight. This is, naturally, posed as a causal bandit problem. The focus is on causal bandits for linear structural equation models (SEMs) and soft interventions. It is assumed that the graph's structure is known, and it has $N$ nodes. Two linear mechanisms, one soft intervention and one observational, are assumed for each node, giving rise to $2^N$ possible interventions. The existing causal bandit algorithms assume that at least the interventional distributions of the reward node's parents are fully specified. However, there are $2^N$ such distributions (one corresponding to each intervention), acquiring which becomes prohibitive even in moderate-sized graphs. This paper dispenses with the assumption of knowing these distributions. Two algorithms are proposed for the frequentist (UCB-based) and Bayesian (Thompson Sampling-based) settings. The key idea of these algorithms is to avoid directly estimating the $2^N$ reward distributions and instead estimate the parameters that fully specify the SEMs (linear in $N$) and use them to compute the rewards. In both algorithms, under boundedness assumptions on noise and the parameter space, the cumulative regrets scale as $\tilde{\cal O} ((2d)^L L \sqrt{T})$, where $d$ is the graph's maximum degree, and $L$ is the length of its longest causal path.

Causal Graphs Underlying Generative Models: Path to Learning with Limited Data

Training generative models that capture rich semantics of the data and interpreting the latent representations encoded by such models are very important problems in unsupervised learning. In this work, we provide a simple algorithm that relies on perturbation experiments on latent codes of a pre-trained generative autoencoder to uncover a causal graph that is implied by the generative model. We leverage pre-trained attribute classifiers and perform perturbation experiments to check for influence of a given latent variable on a subset of attributes. Given this, we show that one can fit an effective causal graph that models a structural equation model between latent codes taken as exogenous variables and attributes taken as observed variables. One interesting aspect is that a single latent variable controls multiple overlapping subsets of attributes unlike conventional approach that tries to impose full independence. Using a pre-trained RNN-based generative autoencoder trained on a dataset of peptide sequences, we demonstrate that the learnt causal graph from our algorithm between various attributes and latent codes can be used to predict a specific property for sequences which are unseen. We compare prediction models trained on either all available attributes or only the ones in the Markov blanket and empirically show that in both the unsupervised and supervised regimes, typically, using the predictor that relies on Markov blanket attributes generalizes better for out-of-distribution sequences.

PAC Generalization via Invariant Representations

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a finite sample setting, we consider the notion of $\epsilon$-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Fourier Representations for Black-Box Optimization over Categorical Variables

Optimization of real-world black-box functions defined over purely categorical variables is an active area of research. In particular, optimization and design of biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, and biotechnology. Standalone search algorithms, such as simulated annealing (SA) and Monte Carlo tree search (MCTS), are typically used for such optimization problems. In order to improve the performance and sample efficiency of such algorithms, we propose to use existing methods in conjunction with a surrogate model for the black-box evaluations over purely categorical variables. To this end, we present two different representations, a group-theoretic Fourier expansion and an abridged one-hot encoded Boolean Fourier expansion. To learn such representations, we consider two different settings to update our surrogate model. First, we utilize an adversarial online regression setting where Fourier characters of each representation are considered as experts and their respective coefficients are updated via an exponential weight update rule each time the black box is evaluated. Second, we consider a Bayesian setting where queries are selected via Thompson sampling and the posterior is updated via a sparse Bayesian regression model (over our proposed representation) with a regularized horseshoe prior. Numerical experiments over synthetic benchmarks as well as real-world RNA sequence optimization and design problems demonstrate the representational power of the proposed methods, which achieve competitive or superior performance compared to state-of-the-art counterparts, while improving the computation cost and/or sample efficiency, substantially.

Auto-Transfer: Learning to Route Transferrable Representations

Knowledge transfer between heterogeneous source and target networks and tasks has received a lot of attention in recent times as large amounts of quality labelled data can be difficult to obtain in many applications. Existing approaches typically constrain the target deep neural network (DNN) feature representations to be close to the source DNNs feature representations, which can be limiting. We, in this paper, propose a novel adversarial multi-armed bandit approach which automatically learns to route source representations to appropriate target representations following which they are combined in meaningful ways to produce accurate target models. We see upwards of 5% accuracy improvements compared with the state-of-the-art knowledge transfer methods on four benchmark (target) image datasets CUB200, Stanford Dogs, MIT67, and Stanford40 where the source dataset is ImageNet. We qualitatively analyze the goodness of our transfer scheme by showing individual examples of the important features our target network focuses on in different layers compared with the (closest) competitors. We also observe that our improvement over other methods is higher for smaller target datasets making it an effective tool for small data applications that may benefit from transfer learning.

Scalable Intervention Target Estimation in Linear Models

This paper considers the problem of estimating the unknown intervention targets in a causal directed acyclic graph from observational and interventional data. The focus is on soft interventions in linear structural equation models (SEMs). Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets even for linear SEMs. This severely limits their scalability and sample complexity. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The pivotal idea is to estimate the intervention sites from the difference between the precision matrices associated with the observational and interventional datasets. It involves repeatedly estimating such sites in different subsets of variables. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class. Consistency, Markov equivalency, and sample complexity are established analytically. Finally, simulation results on both real and synthetic data demonstrate the gains of the proposed approach for scalable causal structure recovery. Implementation of the algorithm and the code to reproduce the simulation results are available at \url{https://github.com/bvarici/intervention-estimation}.

AI Explainability 360: Impact and Design

As artificial intelligence and machine learning algorithms become increasingly prevalent in society, multiple stakeholders are calling for these algorithms to provide explanations. At the same time, these stakeholders, whether they be affected citizens, government regulators, domain experts, or system developers, have different explanation needs. To address these needs, in 2019, we created AI Explainability 360 (Arya et al. 2020), an open source software toolkit featuring ten diverse and state-of-the-art explainability methods and two evaluation metrics. This paper examines the impact of the toolkit with several case studies, statistics, and community feedback. The different ways in which users have experienced AI Explainability 360 have resulted in multiple types of impact and improvements in multiple metrics, highlighted by the adoption of the toolkit by the independent LF AI & Data Foundation. The paper also describes the flexible design of the toolkit, examples of its use, and the significant educational material and documentation available to its users.