Author name cluster

Ali Tajer

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

14 papers

2 author rows

TMLR Journal 2025 Journal Article

Combinatorial Multi-armed Bandits: Arm Selection via Group Testing

Arpan Mukherjee
Shashanka Ubaru
Keerthiram Murugesan
Karthikeyan Shanmugam
Ali Tajer

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a *parameter estimation* routine that sequentially estimates a set of base-arm parameters, and (2) a *super-arm selection* policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an *exact* oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of *group-testing* for selecting the super arms and *quantized* Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be *logarithmic* in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to *at least an exponential* reduction in complexity compared to the oracle-based approaches.

PDF Details

NeurIPS Conference 2025 Conference Paper

Reward-oriented Causal Representation Learning

Zirui Yan
Emre Acartürk
Ali Tajer

Causal representation learning (CRL) is the process of disentangling the *latent* low-dimensional causally-related generating factors underlying high-dimensional observable data. Extensive recent studies have characterized CRL identifiability and *perfect* recovery of the latent variables and their attendant causal graph. This paper introduces the notion of *reward-oriented* CRL, the purpose of which is to move away from perfectly learning the latent representation and instead learning it to the extent needed for optimizing a desired downstream task (reward). In reward-oriented CRL, perfectly learning the latent representation can be excessive; instead, it must be learned at the *coarsest* level sufficient for optimizing the desired task. Reward-oriented CRL is formalized as the optimization of a desired function of the observable data over the space of all possible interventions and focuses on linear causal and transformation models. To sequentially identify the optimal subset of interventions, an adaptive exploration algorithm is designed that learns the latent causal graph and the variables needed to identify the best intervention. It is shown that for an $n$-dimensional latent space and a $d$-dimensional observation space, over a horizon $T$ the algorithm's regret scales as $\tilde O(d^{\frac{1}{3}}n^{\frac{1}{3}}u^{\frac{2}{3}}T^{\frac{2}{3}} + u\sqrt{T})$, where $u$ measures total uncertainty in the graph estimates. Furthermore, an almost-matching lower bound is shown to scale as $\Omega(d^{\frac{1}{3}}n^{\frac{1}{3}}p^{\frac{2}{3}}T^{\frac{2}{3}} + p\sqrt{T})$, in which $u$ is replaced by $p$ that counts the number of causal paths in the graph.

PDF Details

JMLR Journal 2025 Journal Article

Score-based Causal Representation Learning: Linear and General Transformations

Burak Varici
Emre Acartürk
Karthikeyan Shanmugam
Abhishek Kumar
Ali Tajer

This paper addresses intervention-based causal representation learning (CRL) under a general nonparametric latent causal model and an unknown transformation that maps the latent variables to the observed variables. Linear and general transformations are investigated. The paper addresses both the identifiability and achievability aspects. Identifiability refers to determining algorithm-agnostic conditions that ensure the recovery of the true latent causal variables and the underlying latent causal graph. Achievability refers to the algorithmic aspects and addresses designing algorithms that achieve identifiability guarantees. By drawing novel connections between score functions (i.e., the gradients of the logarithm of density functions) and CRL, this paper designs a score-based class of algorithms that ensures both identifiability and achievability. First, the paper focuses on linear transformations and shows that one stochastic hard intervention per node suffices to guarantee identifiability. It also provides partial identifiability guarantees for soft interventions, including identifiability up to mixing with parents for general causal models and perfect recovery of the latent graph for sufficiently nonlinear causal models. Secondly, it focuses on general transformations and demonstrates that two stochastic hard interventions per node are sufficient for identifiability. This is achieved by defining a differentiable loss function whose global optima ensure identifiability for general CRL. Notably, one does not need to know which pair of interventional environments has the same node intervened. Finally, the theoretical results are empirically validated via experiments on structured synthetic data and image data. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2025. ( edit, beta )

PDF Details

NeurIPS Conference 2024 Conference Paper

Interventional Causal Discovery in a Mixture of DAGs

Burak Varıcı
Dmitriy A. Katz
Dennis Wei
Prasanna Sattigeri
Ali Tajer

Causal interactions among a group of variables are often modeled by a single causal graph. In some domains, however, these interactions are best described by multiple co-existing causal graphs, e. g. , in dynamical systems or genomics. This paper addresses the hitherto unknown role of interventions in learning causal interactions among variables governed by a mixture of causal systems, each modeled by one directed acyclic graph (DAG). Causal discovery from mixtures is fundamentally more challenging than single-DAG causal discovery. Two major difficulties stem from (i) an inherent uncertainty about the skeletons of the component DAGs that constitute the mixture and (ii) possibly cyclic relationships across these component DAGs. This paper addresses these challenges and aims to identify edges that exist in at least one component DAG of the mixture, referred to as the *true* edges. First, it establishes matching necessary and sufficient conditions on the size of interventions required to identify the true edges. Next, guided by the necessity results, an adaptive algorithm is designed that learns all true edges using ${\cal O}(n^2)$ interventions, where $n$ is the number of nodes. Remarkably, the size of the interventions is optimal if the underlying mixture model does not contain cycles across its components. More generally, the gap between the intervention size used by the algorithm and the optimal size is quantified. It is shown to be bounded by the *cyclic complexity number* of the mixture model, defined as the size of the minimal intervention that can break the cycles in the mixture, which is upper bounded by the number of cycles among the ancestors of a node.

PDF Details DOI

NeurIPS Conference 2024 Conference Paper

Linear Causal Bandits: Unknown Graph and Soft Interventions

Zirui Yan
Ali Tajer

Designing causal bandit algorithms depends on two central categories of assumptions: (i) the extent of information about the underlying causal graphs and (ii) the extent of information about interventional statistical models. There have been extensive recent advances in dispensing with assumptions on either category. These include assuming known graphs but unknown interventional distributions, and the converse setting of assuming unknown graphs but access to restrictive hard/$\operatorname{do}$ interventions, which removes the stochasticity and ancestral dependencies. Nevertheless, the problem in its general form, i. e. , _unknown_ graph and _unknown_ stochastic intervention models, remains open. This paper addresses this problem and establishes that in a graph with $N$ nodes, maximum in-degree $d$ and maximum causal path length $L$, after $T$ interaction rounds the regret upper bound scales as $\tilde{\mathcal{O}}((cd)^{L-\frac{1}{2}}\sqrt{T} + d + RN)$ where $c>1$ is a constant and $R$ is a measure of intervention power. A universal minimax lower bound is also established, which scales as $\Omega(d^{L-\frac{3}{2}}\sqrt{T})$. Importantly, the graph size $N$ has a diminishing effect on the regret as $T$ grows. These bounds have matching behavior in $T$, exponential dependence on $L$, and polynomial dependence on $d$ (with the gap $d\ $). On the algorithmic aspect, the paper presents a novel way of designing a computationally efficient CB algorithm, addressing a challenge that the existing CB algorithms using soft interventions face.

PDF Details DOI

NeurIPS Conference 2024 Conference Paper

Linear Causal Representation Learning from Unknown Multi-node Interventions

Burak Varıcı
Emre Acartürk
Karthikeyan Shanmugam
Ali Tajer

Despite the multifaceted recent advances in interventional causal representation learning (CRL), they primarily focus on the stylized assumption of single-node interventions. This assumption is not valid in a wide range of applications, and generally, the subset of nodes intervened in an interventional environment is fully unknown. This paper focuses on interventional CRL under unknown multi-node (UMN) interventional environments and establishes the first identifiability results for general latent causal models (parametric or nonparametric) under stochastic interventions (soft or hard) and linear transformation from the latent to observed space. Specifically, it is established that given sufficiently diverse interventional environments, (i) identifiability up to ancestors is possible using only soft interventions, and (ii) perfect identifiability is possible using hard interventions. Remarkably, these guarantees match the best-known results for more restrictive single-node interventions. Furthermore, CRL algorithms are also provided that achieve the identifiability guarantees. A central step in designing these algorithms is establishing the relationships between UMN interventional CRL and score functions associated with the statistical models of different interventional environments. Establishing these relationships also serves as constructive proof of the identifiability guarantees.

PDF Details DOI

NeurIPS Conference 2024 Conference Paper

Sample Complexity of Interventional Causal Representation Learning

Emre Acartürk
Burak Varıcı
Karthikeyan Shanmugam
Ali Tajer

Consider a data-generation process that transforms low-dimensional _latent_ causally-related variables to high-dimensional _observed_ variables. Causal representation learning (CRL) is the process of using the observed data to recover the latent causal variables and the causal structure among them. Despite the multitude of identifiability results under various interventional CRL settings, the existing guarantees apply exclusively to the _infinite-sample_ regime (i. e. , infinite observed samples). This paper establishes the first sample-complexity analysis for the finite-sample regime, in which the interactions between the number of observed samples and probabilistic guarantees on recovering the latent variables and structure are established. This paper focuses on _general_ latent causal models, stochastic _soft_ interventions, and a linear transformation from the latent to the observation space. The identifiability results ensure graph recovery up to ancestors and latent variables recovery up to mixing with parent variables. Specifically, ${\cal O}((\log \frac{1}{\delta})^{4})$ samples suffice for latent graph recovery up to ancestors with probability $1 - \delta$, and ${\cal O}((\frac{1}{\epsilon}\log \frac{1}{\delta})^{4})$ samples suffice for latent causal variables recovery that is $\epsilon$ close to the identifiability class with probability $1 - \delta$.

PDF Details DOI

TMLR Journal 2024 Journal Article

Separability Analysis for Causal Discovery in Mixture of DAGs

Burak Varici
Dmitriy Katz
Dennis Wei
Prasanna Sattigeri
Ali Tajer

Directed acyclic graphs (DAGs) are effective for compactly representing causal systems and specifying the causal relationships among the system's constituents. Specifying such causal relationships in some systems requires a mixture of multiple DAGs -- a single DAG is insufficient. Some examples include time-varying causal systems or aggregated subgroups of a population. Recovering the causal structure of the systems represented by single DAGs is investigated extensively, but it remains mainly open for the systems represented by a mixture of DAGs. A major difference between single- versus mixture-DAG recovery is the existence of node pairs that are separable in the individual DAGs but become inseparable in their mixture. This paper provides the theoretical foundations for analyzing such inseparable node pairs. Specifically, the notion of \emph{emergent edges} is introduced to represent such inseparable pairs that do not exist in the single DAGs but emerge in their mixtures. Necessary conditions for identifying the emergent edges are established. Operationally, these conditions serve as sufficient conditions for separating a pair of nodes in the mixture of DAGs. These results are further extended, and matching necessary and sufficient conditions for identifying the emergent edges in tree-structured DAGs are established. Finally, a novel graphical representation is formalized to specify these conditions, and an algorithm is provided for inferring the learnable causal relations.

PDF Details

JMLR Journal 2023 Journal Article

Causal Bandits for Linear Structural Equation Models

Burak Varici
Karthikeyan Shanmugam
Prasanna Sattigeri
Ali Tajer

This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model to minimize 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 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 majority of 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 or their marginals. 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 $\tilde{\cal O} (d^{L+\frac{1}{2}} \sqrt{NT})$, where $d$ is the graph's maximum degree, and $L$ is the length of its longest causal path. Additionally, a minimax lower of $\Omega(d^{\frac{L}{2}-2}\sqrt{T})$ is presented, which suggests that the achievable and lower bounds conform in their scaling behavior with respect to the horizon $T$ and graph parameters $d$ and $L$. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

PDF Details

AAAI Conference 2023 Conference Paper

When Neural Networks Fail to Generalize? A Model Sensitivity Perspective

Jiajin Zhang
Hanqing Chao
Amit Dhurandhar
Pin-Yu Chen
Ali Tajer
Yangyang Xu
Pingkun Yan

Domain generalization (DG) aims to train a model to perform well in unseen domains under different distributions. This paper considers a more realistic yet more challenging scenario, namely Single Domain Generalization (Single-DG), where only a single source domain is available for training. To tackle this challenge, we first try to understand when neural networks fail to generalize? We empirically ascertain a property of a model that correlates strongly with its generalization that we coin as "model sensitivity". Based on our analysis, we propose a novel strategy of Spectral Adversarial Data Augmentation (SADA) to generate augmented images targeted at the highly sensitive frequencies. Models trained with these hard-to-learn samples can effectively suppress the sensitivity in the frequency space, which leads to improved generalization performance. Extensive experiments on multiple public datasets demonstrate the superiority of our approach, which surpasses the state-of-the-art single-DG methods by up to 2.55%. The source code is available at https://github.com/DIAL-RPI/Spectral-Adversarial-Data-Augmentation.

PDF Details DOI

UAI Conference 2022 Conference Paper

Intervention target estimation in the presence of latent variables

Burak Varici
Karthikeyan Shanmugam 0001
Prasanna Sattigeri
Ali Tajer

This paper considers the problem of estimating unknown intervention targets in causal directed acyclic graphs from observational and interventional data in the presence of latent variables. The focus is on linear structural equation models with soft interventions. The existing approaches to this problem involve performing extensive conditional independence tests, and they estimate the unknown intervention targets alongside learning the structure of the causal model in its entirety. This joint learning approach results in algorithms that are not scalable as graph sizes grow. This paper proposes an approach that does not necessitate learning the entire causal model and focuses on learning only the intervention targets. The key idea of this approach is leveraging the property that interventions impose sparse changes in the precision matrix of a linear model. The proposed framework consists of a sequence of precision difference estimation steps. Furthermore, the necessary knowledge to refine an observational Markov equivalence class (MEC) to an interventional MEC is inferred. Simulation results are provided to illustrate the scalability of the proposed algorithm and compare it with those of the existing approaches.

Details

NeurIPS Conference 2021 Conference Paper

Mean-based Best Arm Identification in Stochastic Bandits under Reward Contamination

Arpan Mukherjee
Ali Tajer
Pin-Yu Chen
Payel Das

This paper investigates the problem of best arm identification in {\sl contaminated} stochastic multi-arm bandits. In this setting, the rewards obtained from any arm are replaced by samples from an adversarial model with probability $\varepsilon$. A fixed confidence (infinite-horizon) setting is considered, where the goal of the learner is to identify the arm with the largest mean. Owing to the adversarial contamination of the rewards, each arm's mean is only partially identifiable. This paper proposes two algorithms, a gap-based algorithm and one based on the successive elimination, for best arm identification in sub-Gaussian bandits. These algorithms involve mean estimates that achieve the optimal error guarantee on the deviation of the true mean from the estimate asymptotically. Furthermore, these algorithms asymptotically achieve the optimal sample complexity. Specifically, for the gap-based algorithm, the sample complexity is asymptotically optimal up to constant factors, while for the successive elimination-based algorithm, it is optimal up to logarithmic factors. Finally, numerical experiments are provided to illustrate the gains of the algorithms compared to the existing baselines.

PDF Details

NeurIPS Conference 2021 Conference Paper

Scalable Intervention Target Estimation in Linear Models

Burak Varici
Karthikeyan Shanmugam
Prasanna Sattigeri
Ali Tajer

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}.

PDF Details

NeurIPS Conference 2019 Conference Paper

Structure Learning with Side Information: Sample Complexity

Saurabh Sihag
Ali Tajer

Graphical models encode the stochastic dependencies among random variables (RVs). The vertices represent the RVs, and the edges signify the conditional dependencies among the RVs. Structure learning is the process of inferring the edges by observing realizations of the RVs, and it has applications in a wide range of technological, social, and biological networks. Learning the structure of graphs when the vertices are treated in isolation from inferential information known about them is well-investigated. In a wide range of domains, however, often there exist additional inferred knowledge about the structure, which can serve as valuable side information. For instance, the gene networks that represent different subtypes of the same cancer share similar edges across all subtypes and also have exclusive edges corresponding to each subtype, rendering partially similar graphical models for gene expression in different cancer subtypes. Hence, an inferential decision regarding a gene network can serve as side information for inferring other related gene networks. When such side information is leveraged judiciously, it can translate to significant improvement in structure learning. Leveraging such side information can be abstracted as inferring structures of distinct graphical models that are {\sl partially} similar. This paper focuses on Ising graphical models, and considers the problem of simultaneously learning the structures of two {\sl partially} similar graphs, where any inference about the structure of one graph offers side information for the other graph. The bounded edge subclass of Ising models is considered, and necessary conditions (information-theoretic ), as well as sufficient conditions (algorithmic) for the sample complexity for achieving a bounded probability of error, are established. Furthermore, specific regimes are identified in which the necessary and sufficient conditions coincide, rendering the optimal sample complexity.

PDF Details