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Mechanistic interpretability aims to provide human-understandable insights into the inner workings of neural network models by examining their internals. Existing approaches typically require significant manual effort and prior knowledge, with strategies tailored to specific tasks. In this work, we take a step toward automating the understanding of the network by investigating the existence of distinct sub-networks. Specifically, we explore a novel automated and task-agnostic approach based on the notion of functionally similar representations within neural networks, reducing the need for human intervention. Our method identifies similar and dissimilar layers in the network, revealing potential sub-components. We achieve this by proposing, for the first time to our knowledge, the use of Gromov-Wasserstein distance, which overcomes challenges posed by varying distributions and dimensionalities across intermediate representations, issues that complicate direct layer-to-layer comparisons. Through experiments on algebraic and language tasks, we observe the emergence of sub-groups within neural network layers corresponding to functional abstractions. Additionally, we find that different training strategies influence the positioning of these sub-groups. Our approach offers meaningful insights into the behavior of neural networks with minimal human and computational cost.

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., Comment: 26 pages

With the boom of machine learning (ML) techniques, software practitioners build ML systems to process the massive volume of streaming data for diverse software engineering tasks such as failure prediction in AIOps. Trained using historical data, such ML models encounter performance degradation caused by concept drift, i.e., data and inter-relationship (concept) changes between training and production. It is essential to use concept rift detection to monitor the deployed ML models and re-train the ML models when needed. In this work, we explore applying state-of-the-art (SOTA) concept drift detection techniques on synthetic and real-world datasets in an industrial setting. Such an industrial setting requires minimal manual effort in labeling and maximal generality in ML model architecture. We find that current SOTA semi-supervised methods not only require significant labeling effort but also only work for certain types of ML models. To overcome such limitations, we propose a novel model-agnostic technique (CDSeer) for detecting concept drift. Our evaluation shows that CDSeer has better precision and recall compared to the state-of-the-art while requiring significantly less manual labeling. We demonstrate the effectiveness of CDSeer at concept drift detection by evaluating it on eight datasets from different domains and use cases. Results from internal deployment of CDSeer on an industrial proprietary dataset show a 57.1% improvement in precision while using 99% fewer labels compared to the SOTA concept drift detection method. The performance is also comparable to the supervised concept drift detection method, which requires 100% of the data to be labeled. The improved performance and ease of adoption of CDSeer are valuable in making ML systems more reliable.

LLMs have shown remarkable capabilities, but precisely controlling their response behavior remains challenging. Existing activation steering methods alter LLM behavior indiscriminately, limiting their practical applicability in settings where selective responses are essential, such as content moderation or domain-specific assistants. In this paper, we propose Conditional Activation Steering (CAST), which analyzes LLM activation patterns during inference to selectively apply or withhold activation steering based on the input context. Our method is based on the observation that different categories of prompts activate distinct patterns in the model's hidden states. Using CAST, one can systematically control LLM behavior with rules like "if input is about hate speech or adult content, then refuse" or "if input is not about legal advice, then refuse." This allows for selective modification of responses to specific content while maintaining normal responses to other content, all without requiring weight optimization. We release an open-source implementation of our framework.

Aligning large language models (LLMs) to value systems has emerged as a significant area of research within the fields of AI and NLP. Currently, this alignment process relies on the availability of high-quality supervised and preference data, which can be both time-consuming and expensive to curate or annotate. In this paper, we introduce a systematic end-to-end methodology for aligning LLMs to the implicit and explicit values represented in unstructured text data. Our proposed approach leverages the use of scalable synthetic data generation techniques to effectively align the model to the values present in the unstructured data. Through two distinct use-cases, we demonstrate the efficiency of our methodology on the Mistral-7B-Instruct model. Our approach credibly aligns LLMs to the values embedded within documents, and shows improved performance against other approaches, as quantified through the use of automatic metrics and win rates.

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.

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

Federated learning (FL) allows clients to collaboratively train a global model without sharing their local data with a server. However, clients' contributions to the server can still leak sensitive information. Differential privacy (DP) addresses such leakage by providing formal privacy guarantees, with mechanisms that add randomness to the clients' contributions. The randomness makes it infeasible to train large transformer-based models, common in modern federated learning systems. In this work, we empirically evaluate the practicality of fine-tuning large scale on-device transformer-based models with differential privacy in a federated learning system. We conduct comprehensive experiments on various system properties for tasks spanning a multitude of domains: speech recognition, computer vision (CV) and natural language understanding (NLU). Our results show that full fine-tuning under differentially private federated learning (DP-FL) generally leads to huge performance degradation which can be alleviated by reducing the dimensionality of contributions through parameter-efficient fine-tuning (PEFT). Our benchmarks of existing DP-PEFT methods show that DP-Low-Rank Adaptation (DP-LoRA) consistently outperforms other methods. An even more promising approach, DyLoRA, which makes the low rank variable, when naively combined with FL would straightforwardly break differential privacy. We therefore propose an adaptation method that can be combined with differential privacy and call it DP-DyLoRA. Finally, we are able to reduce the accuracy degradation and word error rate (WER) increase due to DP to less than 2% and 7% respectively with 1 million clients and a stringent privacy budget of $\epsilon=2$., Comment: 16 pages, 10 figures, 5 tables

We developed a common algorithmic solution addressing the problem of resource-constrained outreach encountered by social change organizations with different missions and operations: Breaking Ground -- an organization that helps individuals experiencing homelessness in New York transition to permanent housing and Leket -- the national food bank of Israel that rescues food from farms and elsewhere to feed the hungry. Specifically, we developed an estimation and optimization approach for partially-observed episodic restless bandits under $k$-step transitions. The results show that our Thompson sampling with Markov chain recovery (via Stein variational gradient descent) algorithm significantly outperforms baselines for the problems of both organizations. We carried out this work in a prospective manner with the express goal of devising a flexible-enough but also useful-enough solution that can help overcome a lack of sustainable impact in data science for social good.

GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use of low bit-width integers to approximate the original entries in a matrix. This allows efficiency gains, but often requires sophisticated techniques to control the rounding error incurred. In this work, we first verify/check that when the low bit-width restriction is removed, for a variety of Transformer-based models, whether integers are sufficient for all GEMMs need -- for {\em both} training and inference stages, and can achieve parity with floating point counterparts. No sophisticated techniques are needed. We find that while a large majority of entries in matrices (encountered in such models) can be easily represented by {\em low} bit-width integers, the existence of a few heavy hitter entries make it difficult to achieve efficiency gains via the exclusive use of low bit-width GEMMs alone. To address this issue, we develop a simple algorithm, Integer Matrix Unpacking (IM-Unpack), to {\em unpack} a matrix with large integer entries into a larger matrix whose entries all lie within the representable range of arbitrarily low bit-width integers. This allows {\em equivalence} with the original GEMM, i.e., the exact result can be obtained using purely low bit-width integer GEMMs. This comes at the cost of additional operations -- we show that for many popular models, this overhead is quite small.

While GPU clusters are the de facto choice for training large deep neural network (DNN) models today, several reasons including ease of workflow, security and cost have led to efforts investigating whether CPUs may be viable for inference in routine use in many sectors of the industry. But the imbalance between the compute capabilities of GPUs and CPUs is huge. Motivated by these considerations, we study a module which is a workhorse within modern DNN architectures, GEMM based Feed Forward Networks (FFNs), and assess the extent to which it can be made compute- (or FLOP-) lite. Specifically, we propose an alternative formulation (we call it LookupFFN) to GEMM based FFNs inspired by the recent studies of using Locality Sensitive Hashing (LSH) to approximate FFNs. Our formulation recasts most essential operations as a memory look-up, leveraging the trade-off between the two resources on any platform: compute and memory (since CPUs offer it in abundance). For RoBERTa language model pretraining, our formulation achieves similar performance compared to GEMM based FFNs, while dramatically reducing the required FLOP. Our development is complemented with a detailed hardware profiling of strategies that will maximize efficiency -- not just on contemporary hardware but on products that will be offered in the near/medium term future. Code is avaiable at \url{https://github.com/mlpen/LookupFFN}., Comment: ICML 2023

The alignment of large language models is usually done by model providers to add or control behaviors that are common or universally understood across use cases and contexts. In contrast, in this article, we present an approach and architecture that empowers application developers to tune a model to their particular values, social norms, laws and other regulations, and orchestrate between potentially conflicting requirements in context. We lay out three main components of such an Alignment Studio architecture: Framers, Instructors, and Auditors that work in concert to control the behavior of a language model. We illustrate this approach with a running example of aligning a company's internal-facing enterprise chatbot to its business conduct guidelines., Comment: 7 pages, 5 figures

Evaluation and ranking of large language models (LLMs) has become an important problem with the proliferation of these models and their impact. Evaluation methods either require human responses which are expensive to acquire or use pairs of LLMs to evaluate each other which can be unreliable. In this paper, we provide a novel perspective where, given a dataset of prompts (viz. questions, instructions, etc.) and a set of LLMs, we rank them without access to any ground truth or reference responses. Inspired by real life where both an expert and a knowledgeable person can identify a novice our main idea is to consider triplets of models, where each one of them evaluates the other two, correctly identifying the worst model in the triplet with high probability. We also analyze our idea and provide sufficient conditions for it to succeed. Applying this idea repeatedly, we propose two methods to rank LLMs. In experiments on different generative tasks (summarization, multiple-choice, and dialog), our methods reliably recover close to true rankings without reference data. This points to a viable low-resource mechanism for practical use., Comment: Accepted to ACL 2024

Given the black box nature of machine learning models, a plethora of explainability methods have been developed to decipher the factors behind individual decisions. In this paper, we introduce a novel problem of black box (probabilistic) explanation certification. We ask the question: Given a black box model with only query access, an explanation for an example and a quality metric (viz. fidelity, stability), can we find the largest hypercube (i.e., $\ell_{\infty}$ ball) centered at the example such that when the explanation is applied to all examples within the hypercube, (with high probability) a quality criterion is met (viz. fidelity greater than some value)? Being able to efficiently find such a \emph{trust region} has multiple benefits: i) insight into model behavior in a \emph{region}, with a \emph{guarantee}; ii) ascertained \emph{stability} of the explanation; iii) \emph{explanation reuse}, which can save time, energy and money by not having to find explanations for every example; and iv) a possible \emph{meta-metric} to compare explanation methods. Our contributions include formalizing this problem, proposing solutions, providing theoretical guarantees for these solutions that are computable, and experimentally showing their efficacy on synthetic and real data., Comment: Accepted to ICML 2024

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field., Comment: Proceedings of the 41st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/.

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 recovering the true latent causal variables and the latent causal graph underlying them. 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 ancestors for general causal models and perfect latent graph recovery for sufficiently non-linear causal models. Secondly, it focuses on general transformations and shows that two stochastic hard interventions per node suffice for identifiability. Notably, one does not need to know which pair of interventional environments have the same node intervened., Comment: (updated literature review) Linear transformations: stronger results than our previous paper Score-based Causal Representation Learning with Interventions (arXiv:2301.08230). General transformations: results also appear in our paper General Identifiability and Achievability for Causal Representation Learning (arXiv:2310.15450) accepted to AISTATS 2024 (oral). arXiv admin note: text overlap with arXiv:2310.15450

Due to their ability to model meaningful higher order relations among a set of entities, higher order network models have emerged recently as a powerful alternative for graph-based network models which are only capable of modeling binary relationships. Message passing paradigm is still dominantly used to learn representations even for higher order network models. While powerful, message passing can have disadvantages during inference, particularly when the higher order connectivity information is missing or corrupted. To overcome such limitations, we propose Topo-MLP, a purely MLP-based simplicial neural network algorithm to learn the representation of elements in a simplicial complex without explicitly relying on message passing. Our framework utilizes a novel Higher Order Neighborhood Contrastive (HONC) loss which implicitly incorporates the simplicial structure into representation learning. Our proposed model's simplicity makes it faster during inference. Moreover, we show that our model is robust when faced with missing or corrupted connectivity structure.

Federated learning is a technique of decentralized machine learning. that allows multiple parties to collaborate and learn a shared model without sharing their raw data. Our paper proposes a federated learning framework for intrusion detection in Internet of Vehicles (IOVs) using the CIC-IDS 2017 dataset. The proposed framework employs SMOTE for handling class imbalance, outlier detection for identifying and removing abnormal observations, and hyperparameter tuning to optimize the model's performance. The authors evaluated the proposed framework using various performance metrics and demonstrated its effectiveness in detecting intrusions with other datasets (KDD-Cup 99 and UNSW- NB-15) and conventional classifiers. Furthermore, the proposed framework can protect sensitive data while achieving high intrusion detection performance.

We consider the problem of \emph{blocked} collaborative bandits 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. Our goal is to design algorithms that maximize the cumulative reward accrued by all the users over time, under the \emph{constraint} that no arm of a user is pulled more than $\mathsf{B}$ times. This problem has been originally considered by \cite{Bresler:2014}, and designing regret-optimal algorithms for it has since remained an open problem. In this work, we propose an algorithm called \texttt{B-LATTICE} (Blocked Latent bAndiTs via maTrIx ComplEtion) that collaborates across users, while simultaneously satisfying the budget constraints, to maximize their cumulative rewards. Theoretically, under certain reasonable assumptions on the latent structure, with $\mathsf{M}$ users, $\mathsf{N}$ arms, $\mathsf{T}$ rounds per user, and $\mathsf{C}=O(1)$ latent clusters, \texttt{B-LATTICE} achieves a per-user regret of $\widetilde{O}(\sqrt{\mathsf{T}(1 + \mathsf{N}\mathsf{M}^{-1})}$ under a budget constraint of $\mathsf{B}=\Theta(\log \mathsf{T})$. These are the first sub-linear regret bounds for this problem, and match the minimax regret bounds when $\mathsf{B}=\mathsf{T}$. Empirically, we demonstrate that our algorithm has superior performance over baselines even when $\mathsf{B}=1$. \texttt{B-LATTICE} runs in phases where in each phase it clusters users into groups and collaborates across users within a group to quickly learn their reward models., Comment: 44 pages, To Appear in NeurIPS 2023

This paper focuses on causal representation learning (CRL) under a general nonparametric latent causal model and a general transformation model that maps the latent data to the observational data. It establishes identifiability and achievability results using two hard uncoupled interventions per node in the latent causal graph. Notably, one does not know which pair of intervention environments have the same node intervened (hence, uncoupled). For identifiability, the paper establishes that perfect recovery of the latent causal model and variables is guaranteed under uncoupled interventions. For achievability, an algorithm is designed that uses observational and interventional data and recovers the latent causal model and variables with provable guarantees. This algorithm leverages score variations across different environments to estimate the inverse of the transformer and, subsequently, the latent variables. The analysis, additionally, recovers the identifiability result for two hard coupled interventions, that is when metadata about the pair of environments that have the same node intervened is known. This paper also shows that when observational data is available, additional faithfulness assumptions that are adopted by the existing literature are unnecessary., Comment: Accepted to AISTATS 2024 (oral presentation). Also appeared at CRL Workshop @ NeurIPS 2023 (oral presentation) titled as "Score-based Causal Representation Learning: Nonparametric Identifiability"

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples., Comment: Published as a conference paper at The Twelfth International Conference on Learning Representations (ICLR 2024) & Oral Presentation at Regulatable ML @ NeurIPS 2023

Covariate shift in the test data is a common practical phenomena that can significantly downgrade both the accuracy and the fairness performance of the model. Ensuring fairness across different sensitive groups under covariate shift is of paramount importance due to societal implications like criminal justice. We operate in the unsupervised regime where only a small set of unlabeled test samples along with a labeled training set is available. Towards improving fairness under this highly challenging yet realistic scenario, we make three contributions. First is a novel composite weighted entropy based objective for prediction accuracy which is optimized along with a representation matching loss for fairness. We experimentally verify that optimizing with our loss formulation outperforms a number of state-of-the-art baselines in the pareto sense with respect to the fairness-accuracy tradeoff on several standard datasets. Our second contribution is a new setting we term Asymmetric Covariate Shift that, to the best of our knowledge, has not been studied before. Asymmetric covariate shift occurs when distribution of covariates of one group shifts significantly compared to the other groups and this happens when a dominant group is over-represented. While this setting is extremely challenging for current baselines, We show that our proposed method significantly outperforms them. Our third contribution is theoretical, where we show that our weighted entropy term along with prediction loss on the training set approximates test loss under covariate shift. Empirically and through formal sample complexity bounds, we show that this approximation to the unseen test loss does not depend on importance sampling variance which affects many other baselines., Comment: Accepted at The 38th Annual AAAI Conference on Artificial Intelligence (AAAI 2024)

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.

Learning paradigms based purely on offline data as well as those based solely on sequential online learning have been well-studied in the literature. In this paper, we consider combining offline data with online learning, an area less studied but of obvious practical importance. We consider the stochastic $K$-armed bandit problem, where our goal is to identify the arm with the highest mean in the presence of relevant offline data, with confidence $1-\delta$. We conduct a lower bound analysis on policies that provide such $1-\delta$ probabilistic correctness guarantees. We develop algorithms that match the lower bound on sample complexity when $\delta$ is small. Our algorithms are computationally efficient with an average per-sample acquisition cost of $\tilde{O}(K)$, and rely on a careful characterization of the optimality conditions of the lower bound problem., Comment: 45 pages, 5 figures

Length generalization, the ability to generalize from small training context sizes to larger ones, is a critical challenge in the development of Transformer-based language models. Positional encoding (PE) has been identified as a major factor influencing length generalization, but the exact impact of different PE schemes on extrapolation in downstream tasks remains unclear. In this paper, we conduct a systematic empirical study comparing the length generalization performance of decoder-only Transformers with five different position encoding approaches including Absolute Position Embedding (APE), T5's Relative PE, ALiBi, and Rotary, in addition to Transformers without positional encoding (NoPE). Our evaluation encompasses a battery of reasoning and mathematical tasks. Our findings reveal that the most commonly used positional encoding methods, such as ALiBi, Rotary, and APE, are not well suited for length generalization in downstream tasks. More importantly, NoPE outperforms other explicit positional encoding methods while requiring no additional computation. We theoretically demonstrate that NoPE can represent both absolute and relative PEs, but when trained with SGD, it mostly resembles T5's relative PE attention patterns. Finally, we find that scratchpad is not always helpful to solve length generalization and its format highly impacts the model's performance. Overall, our work suggests that explicit position embeddings are not essential for decoder-only Transformers to generalize well to longer sequences., Comment: Accepted at NeurIPS 2023; 15 pages and 22 pages Appendix

Training a Named Entity Recognition (NER) model often involves fixing a taxonomy of entity types. However, requirements evolve and we might need the NER model to recognize additional entity types. A simple approach is to re-annotate entire dataset with both existing and additional entity types and then train the model on the re-annotated dataset. However, this is an extremely laborious task. To remedy this, we propose a novel approach called Partial Label Model (PLM) that uses only partially annotated datasets. We experiment with 6 diverse datasets and show that PLM consistently performs better than most other approaches (0.5 - 2.5 F1), including in novel settings for taxonomy expansion not considered in prior work. The gap between PLM and all other approaches is especially large in settings where there is limited data available for the additional entity types (as much as 11 F1), thus suggesting a more cost effective approaches to taxonomy expansion.

This study aims to relate the time-frequency patterns of acoustic emission (AE) and other multi-modal sensor data collected in a hybrid directed energy deposition (DED) process to the pore formations at high spatial (0.5 mm) and time (< 1ms) resolutions. Adapting an explainable AI method in LIME (Local Interpretable Model-Agnostic Explanations), certain high-frequency waveform signatures of AE are to be attributed to two major pathways for pore formation in a DED process, namely, spatter events and insufficient fusion between adjacent printing tracks from low heat input. This approach opens an exciting possibility to predict, in real-time, the presence of a pore in every voxel (0.5 mm in size) as they are printed, a major leap forward compared to prior efforts. Synchronized multimodal sensor data including force, AE, vibration and temperature were gathered while an SS316L material sample was printed and subsequently machined. A deep convolution neural network classifier was used to identify the presence of pores on a voxel surface based on time-frequency patterns (spectrograms) of the sensor data collected during the process chain. The results suggest signals collected during DED were more sensitive compared to those from machining for detecting porosity in voxels (classification test accuracy of 87%). The underlying explanations drawn from LIME analysis suggests that energy captured in high frequency AE waveforms are 33% lower for porous voxels indicating a relatively lower laser-material interaction in the melt pool, and hence insufficient fusion and poor overlap between adjacent printing tracks. The porous voxels for which spatter events were prevalent during printing had about 27% higher energy contents in the high frequency AE band compared to other porous voxels. These signatures from AE signal can further the understanding of pore formation from spatter and insufficient fusion.

Ensuring trustworthiness in machine learning (ML) models is a multi-dimensional task. In addition to the traditional notion of predictive performance, other notions such as privacy, fairness, robustness to distribution shift, adversarial robustness, interpretability, explainability, and uncertainty quantification are important considerations to evaluate and improve (if deficient). However, these sub-disciplines or 'pillars' of trustworthiness have largely developed independently, which has limited us from understanding their interactions in real-world ML pipelines. In this paper, focusing specifically on compositions of functions arising from the different pillars, we aim to reduce this gap, develop new insights for trustworthy ML, and answer questions such as the following. Does the composition of multiple fairness interventions result in a fairer model compared to a single intervention? How do bias mitigation algorithms for fairness affect local post-hoc explanations? Does a defense algorithm for untargeted adversarial attacks continue to be effective when composed with a privacy transformation? Toward this end, we report initial empirical results and new insights from 9 different compositions of functions (or pipelines) on 7 real-world datasets along two trustworthy dimensions - fairness and explainability. We also report progress, and implementation choices, on an extensible composer tool to encourage the combination of functionalities from multiple pillars. To-date, the tool supports bias mitigation algorithms for fairness and post-hoc explainability methods. We hope this line of work encourages the thoughtful consideration of multiple pillars when attempting to formulate and resolve a trustworthiness problem.

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.

A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. To address the problem, we devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries}. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is provided by a probabilistic classification model. The classification model is adaptively updated and used to predict where the (unlabelled) features have a high dependency on labels; labeling the ``high-dependency'' features leads to the increased power of the proposed testing framework. In theory, we provide the proof that our framework produces an \emph{anytime-valid} $p$-value. In addition, we characterize the proposed framework's gain in testing power by analyzing the mutual information between the feature and label variables in asymptotic and finite-sample scenarios. In practice, we introduce an instantiation of our framework and evaluate it using several experiments; the experiments on the synthetic, MNIST, and application-specific datasets demonstrate that the testing power of the instantiated active sequential test significantly increases while the Type I error is under control.

This paper studies the 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 (ii) determining the directed acyclic graph (DAG) underlying the latent variables. Sufficient conditions for DAG recovery are established, and it is shown that a large class of non-linear models in the latent space (e.g., causal mechanisms parameterized by two-layer neural networks) satisfy these conditions. These sufficient conditions ensure that the effect of an intervention can be detected correctly from changes in the score. Capitalizing on this property, recovering a valid transformation is facilitated by the following key property: any valid transformation renders latent variables' score function to necessarily have the minimal variations across different interventional environments. This property is leveraged for perfect recovery of the latent DAG structure using only \emph{soft} interventions. For the special case of stochastic \emph{hard} interventions, with an additional hypothesis testing step, one can also uniquely recover the linear transformation up to scaling and a valid causal ordering., Comment: This version outlines large classes of non-linear causal models in the latent space for which our assumptions hold. It also discusses the latest updates of related literature

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 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., Comment: 48 pages. Accepted to AISTATS 2023. Added Experiments

Predictive uncertainty-a model's self awareness regarding its accuracy on an input-is key for both building robust models via training interventions and for test-time applications such as selective classification. We propose a novel instance-conditioned reweighting approach that captures predictive uncertainty using an auxiliary network and unifies these train- and test-time applications. The auxiliary network is trained using a meta-objective in a bilevel optimization framework. A key contribution of our proposal is the meta-objective of minimizing the dropout variance, an approximation of Bayesian Predictive uncertainty. We show in controlled experiments that we effectively capture the diverse specific notions of uncertainty through this meta-objective, while previous approaches only capture certain aspects. These results translate to significant gains in real-world settings-selective classification, label noise, domain adaptation, calibration-and across datasets-Imagenet, Cifar100, diabetic retinopathy, Camelyon, WILDs, Imagenet-C,-A,-R, Clothing1M, etc. For Diabetic Retinopathy, we see upto 3.4%/3.3% accuracy and AUC gains over SOTA in selective classification. We also improve upon large-scale pretrained models such as PLEX.

We introduce equi-tuning, a novel fine-tuning method that transforms (potentially non-equivariant) pretrained models into group equivariant models while incurring minimum $L_2$ loss between the feature representations of the pretrained and the equivariant models. Large pretrained models can be equi-tuned for different groups to satisfy the needs of various downstream tasks. Equi-tuned models benefit from both group equivariance as an inductive bias and semantic priors from pretrained models. We provide applications of equi-tuning on three different tasks: image classification, compositional generalization in language, and fairness in natural language generation (NLG). We also provide a novel group-theoretic definition for fairness in NLG. The effectiveness of this definition is shown by testing it against a standard empirical method of fairness in NLG. We provide experimental results for equi-tuning using a variety of pretrained models: Alexnet, Resnet, VGG, and Densenet for image classification; RNNs, GRUs, and LSTMs for compositional generalization; and GPT2 for fairness in NLG. We test these models on benchmark datasets across all considered tasks to show the generality and effectiveness of the proposed method.

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. 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 $L$., Comment: 61 pages; new to this version: added lower bounds and relaxed assumptions

Training generative models that capture rich semantics of the data and interpreting the latent representations encoded by such models are very important problems in un-/self-supervised 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 an attribute graph that is implied by the generative model. We 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 graphical model 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 approaches that try to impose full independence. Using a pre-trained generative autoencoder trained on a large dataset of small molecules, we demonstrate that the graphical model between various molecular attributes and latent codes learned by our algorithm can be used to predict a specific property for molecules which are drawn from a different distribution. We compare prediction models trained on various feature subsets chosen by simple baselines, as well as existing causal discovery and sparse learning/feature selection methods, with the ones in the derived Markov blanket from our method. Results show empirically that the predictor that relies on our Markov blanket attributes is robust to distribution shifts when transferred or fine-tuned with a few samples from the new distribution, especially when training data is limited., Comment: New experiments; reframed contributions

Federated Learning (FL) enables training state-of-the-art Automatic Speech Recognition (ASR) models on user devices (clients) in distributed systems, hence preventing transmission of raw user data to a central server. A key challenge facing practical adoption of FL for ASR is obtaining ground-truth labels on the clients. Existing approaches rely on clients to manually transcribe their speech, which is impractical for obtaining large training corpora. A promising alternative is using semi-/self-supervised learning approaches to leverage unlabelled user data. To this end, we propose FedNST, a novel method for training distributed ASR models using private and unlabelled user data. We explore various facets of FedNST, such as training models with different proportions of labelled and unlabelled data, and evaluate the proposed approach on 1173 simulated clients. Evaluating FedNST on LibriSpeech, where 960 hours of speech data is split equally into server (labelled) and client (unlabelled) data, showed a 22.5% relative word error rate reduction} (WERR) over a supervised baseline trained only on server data., Comment: Accepted at Interspeech 2022

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{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 {\em 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 \textit{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.

Multilingual evaluation benchmarks usually contain limited high-resource languages and do not test models for specific linguistic capabilities. CheckList is a template-based evaluation approach that tests models for specific capabilities. The CheckList template creation process requires native speakers, posing a challenge in scaling to hundreds of languages. In this work, we explore multiple approaches to generate Multilingual CheckLists. We device an algorithm - Template Extraction Algorithm (TEA) for automatically extracting target language CheckList templates from machine translated instances of a source language templates. We compare the TEA CheckLists with CheckLists created with different levels of human intervention. We further introduce metrics along the dimensions of cost, diversity, utility, and correctness to compare the CheckLists. We thoroughly analyze different approaches to creating CheckLists in Hindi. Furthermore, we experiment with 9 more different languages. We find that TEA followed by human verification is ideal for scaling Checklist-based evaluation to multiple languages while TEA gives a good estimates of model performance., Comment: Accepted to Findings of AACL-IJCNLP 2022

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.

Federated Learning (FL) is a privacy preserving machine learning scheme, where training happens with data federated across devices and not leaving them to sustain user privacy. This is ensured by making the untrained or partially trained models to reach directly the individual devices and getting locally trained "on-device" using the device owned data, and the server aggregating all the partially trained model learnings to update a global model. Although almost all the model learning schemes in the federated learning setup use gradient descent, there are certain characteristic differences brought about by the non-IID nature of the data availability, that affects the training in comparison to the centralized schemes. In this paper, we discuss the various factors that affect the federated learning training, because of the non-IID distributed nature of the data, as well as the inherent differences in the federating learning approach as against the typical centralized gradient descent techniques. We empirically demonstrate the effect of number of samples per device and the distribution of output labels on federated learning. In addition to the privacy advantage we seek through federated learning, we also study if there is a cost advantage while using federated learning frameworks. We show that federated learning does have an advantage in cost when the model sizes to be trained are not reasonably large. All in all, we present the need for careful design of model for both performance and cost., Comment: 15 pages, 7 figures, 1 table

Post-hoc explanations for black box models have been studied extensively in classification and regression settings. However, explanations for models that output similarity between two inputs have received comparatively lesser attention. In this paper, we provide model agnostic local explanations for similarity learners applicable to tabular and text data. We first propose a method that provides feature attributions to explain the similarity between a pair of inputs as determined by a black box similarity learner. We then propose analogies as a new form of explanation in machine learning. Here the goal is to identify diverse analogous pairs of examples that share the same level of similarity as the input pair and provide insight into (latent) factors underlying the model's prediction. The selection of analogies can optionally leverage feature attributions, thus connecting the two forms of explanation while still maintaining complementarity. We prove that our analogy objective function is submodular, making the search for good-quality analogies efficient. We apply the proposed approaches to explain similarities between sentences as predicted by a state-of-the-art sentence encoder, and between patients in a healthcare utilization application. Efficacy is measured through quantitative evaluations, a careful user study, and examples of explanations.

Knowledge transfer between heterogeneous source and target networks and tasks has received a lot of attention in recent times as large amounts of quality labeled 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 that 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 focused on by our target network at 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., Comment: Camera ready ICLR 2022

Locally interpretable model agnostic explanations (LIME) method is one of the most popular methods used to explain black-box models at a per example level. Although many variants have been proposed, few provide a simple way to produce high fidelity explanations that are also stable and intuitive. In this work, we provide a novel perspective by proposing a model agnostic local explanation method inspired by the invariant risk minimization (IRM) principle -- originally proposed for (global) out-of-distribution generalization -- to provide such high fidelity explanations that are also stable and unidirectional across nearby examples. Our method is based on a game theoretic formulation where we theoretically show that our approach has a strong tendency to eliminate features where the gradient of the black-box function abruptly changes sign in the locality of the example we want to explain, while in other cases it is more careful and will choose a more conservative (feature) attribution, a behavior which can be highly desirable for recourse. Empirically, we show on tabular, image and text data that the quality of our explanations with neighborhoods formed using random perturbations are much better than LIME and in some cases even comparable to other methods that use realistic neighbors sampled from the data manifold. This is desirable given that learning a manifold to either create realistic neighbors or to project explanations is typically expensive or may even be impossible. Moreover, our algorithm is simple and efficient to train, and can ascertain stable input features for local decisions of a black-box without access to side information such as a (partial) causal graph as has been seen in some recent works., Comment: Accepted to NeurIPS 2023

Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are easily measured whereas sample labels are unknown and costly to obtain. Accordingly, we devise a three-stage framework in service of performing an effective two-sample test with only a small number of sample label queries: first, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; second, a novel query scheme dubbed \emph{bimodal query} is used to query labels of samples from both classes, and last, the classical Friedman-Rafsky (FR) two-sample test is performed on the queried samples. Theoretical analysis and extensive experiments performed on several datasets demonstrate that the proposed test controls the Type I error and has decreased Type II error relative to uniform querying and certainty-based querying. Source code for our algorithms and experimental results is available at \url{https://github.com/wayne0908/Label-Efficient-Two-Sample}., Comment: Accepted to the 38th conference on Uncertainty in Artificial Intelligence (UAI2022)

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}., Comment: 23 pages, 4 figures, NeurIPS 2021