Tianyi Peng

Vivek F. Farias, Andrew A. Li, Tianyi Peng et al.

We consider experiments in dynamical systems where interventions on some experimental units impact other units through a limiting constraint (such as a limited inventory). Despite outsize practical importance, the best estimators for this `Markovian' interference problem are largely heuristic in nature, and their bias is not well understood. We formalize the problem of inference in such experiments as one of policy evaluation. Off-policy estimators, while unbiased, apparently incur a large penalty in variance relative to state-of-the-art heuristics. We introduce an on-policy estimator: the Differences-In-Q's (DQ) estimator. We show that the DQ estimator can in general have exponentially smaller variance than off-policy evaluation. At the same time, its bias is second order in the impact of the intervention. This yields a striking bias-variance tradeoff so that the DQ estimator effectively dominates state-of-the-art alternatives. From a theoretical perspective, we introduce three separate novel techniques that are of independent interest in the theory of Reinforcement Learning (RL). Our empirical evaluation includes a set of experiments on a city-scale ride-hailing simulator.

Ang Li, Haozhe Chen, Hongseok Namkoong et al.

The use of large language models (LLMs) to simulate human behavior has gained significant attention, particularly through personas that approximate individual characteristics. Persona-based simulations hold promise for transforming disciplines that rely on population-level feedback, including social science, economic analysis, marketing research, and business operations. Traditional methods to collect realistic persona data face significant challenges. They are prohibitively expensive and logistically challenging due to privacy constraints, and often fail to capture multi-dimensional attributes, particularly subjective qualities. Consequently, synthetic persona generation with LLMs offers a scalable, cost-effective alternative. However, current approaches rely on ad hoc and heuristic generation techniques that do not guarantee methodological rigor or simulation precision, resulting in systematic biases in downstream tasks. Through extensive large-scale experiments including presidential election forecasts and general opinion surveys of the U.S. population, we reveal that these biases can lead to significant deviations from real-world outcomes. Our findings underscore the need to develop a rigorous science of persona generation and outline the methodological innovations, organizational and institutional support, and empirical foundations required to enhance the reliability and scalability of LLM-driven persona simulations. To support further research and development in this area, we have open-sourced approximately one million generated personas, available for public access and analysis at https://huggingface.co/datasets/Tianyi-Lab/Personas.

Wenyue Hua, Sripad Karne, Qian Xie et al.

AI agents are increasingly deployed in real-world applications, including systems such as Manus, OpenClaw, and coding agents. Existing research has primarily focused on \emph{server-side} efficiency, proposing methods such as caching, speculative execution, traffic scheduling, and load balancing to reduce the cost of serving agentic workloads. However, as users increasingly construct agents by composing local tools, remote APIs, and diverse models, an equally important optimization problem arises on the client side. Client-side optimization asks how developers should allocate the resources available to them, including model choice, local tools, and API budget across pipeline stages, subject to application-specific quality, cost, and latency constraints. Because these objectives depend on the task and deployment setting, they cannot be determined by server-side systems alone. We introduce AgentOpt, the first framework-agnostic Python package for client-side agent optimization. We first study model selection, a high-impact optimization lever in multi-step agent pipelines. Given a pipeline and a small evaluation set, the goal is to find the most cost-effective assignment of models to pipeline roles. This problem is consequential in practice: at matched accuracy, the cost gap between the best and worst model combinations can reach 13--32$\times$ in our experiments. To efficiently explore the exponentially growing combination space, AgentOpt implements eight search algorithms, including Arm Elimination, Epsilon-LUCB, Threshold Successive Elimination, and Bayesian Optimization. Across four benchmarks, Arm Elimination recovers near-optimal accuracy while reducing evaluation budget by 24--67\% relative to brute-force search on three of four tasks. Code and benchmark results available at https://agentoptimizer.github.io/agentopt/.

Wenyue Hua, Tianyi Peng, Chi Wang et al.

Prior work on trustworthy AI emphasizes model-internal properties such as bias mitigation, adversarial robustness, and interpretability. As AI systems evolve into autonomous agents deployed in open environments and increasingly connected to payments or assets, the operational meaning of trust shifts to end-to-end outcomes: whether an agent completes tasks, follows user intent, and avoids failures that cause material or psychological harm. These risks are fundamentally product-level and cannot be eliminated by technical safeguards alone because agent behavior is inherently stochastic. To address this gap between model-level reliability and user-facing assurance, we propose a complementary framework based on risk management. Drawing inspiration from financial underwriting, we introduce the \textbf{Agentic Risk Standard (ARS)}, a payment settlement standard for AI-mediated transactions. ARS integrates risk assessment, underwriting, and compensation into a single transaction framework that protects users when interacting with agents. Under ARS, users receive predefined and contractually enforceable compensation in cases of execution failure, misalignment, or unintended outcomes. This shifts trust from an implicit expectation about model behavior to an explicit, measurable, and enforceable product guarantee. We also present a simulation study analyzing the social benefits of applying ARS to agentic transactions. ARS's implementation can be found at https://github.com/t54-labs/AgenticRiskStandard.

Akshit Kumar, Tianyi Peng, Yuhang Wu et al.

Large language models (LLMs) have exhibited expert-level capabilities across various domains. However, their abilities to solve problems in Operations Research (OR) -- the analysis and optimization of mathematical models derived from real-world problems or their verbal descriptions -- remain underexplored. In this work, we take a first step toward evaluating LLMs' abilities to solve stochastic modeling problems, a core class of OR problems characterized by uncertainty and typically involving tools from probability, statistics, and stochastic processes. We manually procure a representative set of graduate-level homework and doctoral qualification-exam problems and test LLMs' abilities to solve them. We further leverage SimOpt, an open-source library of simulation-optimization problems and solvers, to investigate LLMs' abilities to make real-world decisions under uncertainty. Our results show that, though a nontrivial amount of work is still needed to reliably automate the stochastic modeling pipeline in reality, state-of-the-art LLMs demonstrate proficiency on par with human experts in both classroom and practical settings. These findings highlight the potential of building AI agents that assist OR researchers and amplify the real-world impact of OR through automation.

Jackie Baek, Yaopeng Fu, Will Ma et al.

Inventory control is a fundamental operations problem in which ordering decisions are traditionally guided by theoretically grounded operations research (OR) algorithms. However, such algorithms often rely on rigid modeling assumptions and can perform poorly when demand distributions shift or relevant contextual information is unavailable. Recent advances in large language models (LLMs) have generated interest in AI agents that can reason flexibly and incorporate rich contextual signals, but it remains unclear how best to incorporate LLM-based methods into traditional decision-making pipelines. We study how OR algorithms, LLMs, and humans can interact and complement each other in a multi-period inventory control setting. We construct InventoryBench, a benchmark of over 1,000 inventory instances spanning both synthetic and real-world demand data, designed to stress-test decision rules under demand shifts, seasonality, and uncertain lead times. Through this benchmark, we find that OR-augmented LLM methods outperform either method in isolation, suggesting that these methods are complementary rather than substitutes. We further investigate the role of humans through a controlled classroom experiment that embeds LLM recommendations into a human-in-the-loop decision pipeline. Contrary to prior findings that human-AI collaboration can degrade performance, we show that, on average, human-AI teams achieve higher profits than either humans or AI agents operating alone. Beyond this population-level finding, we formalize an individual-level complementarity effect and derive a distribution-free lower bound on the fraction of individuals who benefit from AI collaboration; empirically, we find this fraction to be substantial.

Ayeong Lee, Ethan Che, Tianyi Peng

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response, recent works have sought to decrease response lengths through simple prompting strategies (e.g. 'be concise'). In this work, we conduct the first systematic study of the relationship between reasoning length and model performance across a diverse range of compression instructions (e.g. 'use 10 words or less' or 'remove all punctuation'). In doing so, we discover a universal tradeoff between reasoning length and accuracy that persists across even very distinct reasoning chains. We demonstrate that this tradeoff emerges from a sharp threshold behavior at the question level: each task has an intrinsic 'token complexity' - a minimal number of tokens required for successful problem-solving. We show how token complexity enables us to compute information-theoretic limits on the accuracy-compression tradeoff, and find that prompt-based compression strategies operate far from these theoretical limits. This suggests there may be significant room for improvement and our framework provides a benchmark to help researchers evaluate progress in reasoning efficiency. Our work also highlights the importance of adaptive compression -- giving shorter responses for easier questions -- and we show that token complexity is a useful tool for measuring this capability.

Olivier Toubia, George Z. Gui, Tianyi Peng et al.

LLM-based digital twin simulation, where large language models are used to emulate individual human behavior, holds great promise for research in AI, social science, and digital experimentation. However, progress in this area has been hindered by the scarcity of real, individual-level datasets that are both large and publicly available. This lack of high-quality ground truth limits both the development and validation of digital twin methodologies. To address this gap, we introduce a large-scale, public dataset designed to capture a rich and holistic view of individual human behavior. We survey a representative sample of $N = 2,058$ participants (average 2.42 hours per person) in the US across four waves with 500 questions in total, covering a comprehensive battery of demographic, psychological, economic, personality, and cognitive measures, as well as replications of behavioral economics experiments and a pricing survey. The final wave repeats tasks from earlier waves to establish a test-retest accuracy baseline. Initial analyses suggest the data are of high quality and show promise for constructing digital twins that predict human behavior well at the individual and aggregate levels. By making the full dataset publicly available, we aim to establish a valuable testbed for the development and benchmarking of LLM-based persona simulations. Beyond LLM applications, due to its unique breadth and scale the dataset also enables broad social science research, including studies of cross-construct correlations and heterogeneous treatment effects.

Yueying Li, Jim Dai, Tianyi Peng

As demand for Large Language Models (LLMs) and AI agents rapidly grows, optimizing systems for efficient LLM inference becomes critical. While significant efforts have focused on system-level engineering, little is explored from a mathematical modeling and queuing perspective. In this paper, we aim to develop the queuing fundamentals for large language model (LLM) inference, bridging the gap between the queueing theory and LLM system communities. In particular, we study the throughput aspect in LLM inference systems. We prove that a large class of 'work-conserving' scheduling algorithms can achieve maximum throughput for individual inference LLM engine, highlighting 'work-conserving' as a key design principle in practice. In a network of LLM agents, work-conserving scheduling alone is insufficient, particularly when facing specific workload structures and multi-class workflows that require more sophisticated scheduling strategies. Evaluations of real-world systems show that Orca and Sarathi-serve are throughput-optimal, reassuring practitioners, while FasterTransformer and vanilla vLLM are not maximally stable and should be used with caution. Our results highlight the substantial benefits that the queueing community can offer in improving LLM inference systems and call for more interdisciplinary development.

Yang Xiao, Tianyi Peng, Rohan Kumar Das et al.

Keyword spotting (KWS) offers a vital mechanism to identify spoken commands in voice-enabled systems, where user demands often shift, requiring models to learn new keywords continually over time. However, a major problem is catastrophic forgetting, where models lose their ability to recognize earlier keywords. Although several continual learning methods have proven their usefulness for reducing forgetting, most existing approaches depend on storing and revisiting old data to combat catastrophic forgetting. Though effective, these methods face two practical challenges: 1) privacy risks from keeping user data and 2) large memory and time consumption that limit deployment on small devices. To address these issues, we propose an exemplar-free Analytic Continual Learning (AnalyticKWS) method that updates model parameters without revisiting earlier data. Inspired by efficient learning principles, AnalyticKWS computes a closed-form analytical solution for model updates and requires only a single epoch of adaptation for incoming keywords. AnalyticKWS demands fewer computational resources by avoiding gradient-based updates and does not store old data. By eliminating the need for back-propagation during incremental learning, the model remains lightweight and efficient. As a result, AnalyticKWS meets the challenges mentioned earlier and suits resource-limited settings well. Extensive experiments on various datasets and settings show that AnalyticKWS consistently outperforms existing continual learning methods.

Grace Jiarui Fan, Chengpiao Huang, Tianyi Peng et al.

AI-based persona simulation -- often referred to as digital twin simulation -- is increasingly used for market research, recommender systems, and social sciences. Despite their flexibility, large language models (LLMs) often exhibit systematic bias and miscalibration relative to real human behavior, limiting their reliability. Inspired by synthetic control methods from causal inference, we propose SYN-DIGITS (SYNthetic Control Framework for Calibrated DIGItal Twin Simulation), a principled and lightweight calibration framework that learns latent structure from digital-twin responses and transfers it to align predictions with human ground truth. SYN-DIGITS operates as a post-processing layer on top of any LLM-based simulator and thus is model-agnostic. We develop a latent factor model that formalizes when and why calibration succeeds through latent space alignment conditions, and we systematically evaluate ten calibration methods across thirteen persona constructions, three LLMs, and two datasets. SYN-DIGITS supports both individual-level and distributional simulation for previously unseen questions and unobserved populations, with provable error guarantees. Experiments show that SYN-DIGITS achieves up to 50% relative improvements in individual-level correlation and 50--90% relative reductions in distributional discrepancy compared to uncalibrated baselines.

Nikos Pagonas, Matthew Lou, Tianyi Peng et al.

Agentic workflows interleave configurable LLM stages with tool stages and often include retries or refinement loops. Existing workflow managers profile full workflow configurations offline and assign each request a static workflow-level plan that binds each configurable LLM stage to a single model, reuses that model across repeated loop iterations, and does not revisit those choices at runtime. We present VineLM, a workflow manager that enables fine-grained control by choosing the model for each stage invocation as execution unfolds under request-level objectives such as maximizing accuracy under cost or latency budgets. VineLM represents feasible executions as an annotated trie of model-choice prefixes and uses checkpointing and cascade profiling to estimate path accuracy, cost, and latency without exhaustively profiling every request on every path. At runtime, VineLM re-roots the trie after each stage invocation and replans over the remaining subtrie using the realized execution prefix and remaining latency budget. On NL2SQL and math reasoning workflows, VineLM improves the cost-latency-accuracy frontier over coarse workflow-level baselines, achieving up to 18% higher accuracy at the same per-request budget with its sparse profiling reducing offline profiling cost by 98-99.8% when compared to exhaustive profiling.

Naimeng Ye, Arnav Ahuja, Georgios Liargkovas et al.

Despite growing interest in AI agents across industry and academia, their execution in an environment is often slow, hampering training, evaluation, and deployment. For example, a game of chess between two state-of-the-art agents may take hours. A critical bottleneck is that agent behavior unfolds sequentially: each action requires an API call, and these calls can be time-consuming. Inspired by speculative execution in microprocessors and speculative decoding in LLM inference, we propose speculative actions, a lossless framework for general agentic systems that predicts likely actions using faster models, enabling multiple steps to be executed in parallel. We evaluate this framework across three agentic environments: gaming, e-commerce, web search, and a "lossy" extension for an operating systems environment. In all cases, speculative actions achieve substantial accuracy in next-action prediction (up to 55%), translating into significant reductions in end-to-end latency. Moreover, performance can be further improved through stronger guessing models, top-K action prediction, multi-step speculation, and uncertainty-aware optimization, opening a promising path toward deploying low-latency agentic systems in the real world.

Thomson Yen, Andrew Wei Tung Siah, Haozhe Chen et al.

Careful curation of data sources can significantly improve the performance of LLM pre-training, but predominant approaches rely heavily on intuition or costly trial-and-error, making them difficult to generalize across different data domains and downstream tasks. Although scaling laws can provide a principled and general approach for data curation, standard deterministic extrapolation from small-scale experiments to larger scales requires strong assumptions on the reliability of such extrapolation, whose brittleness has been highlighted in prior works. In this paper, we introduce a $\textit{probabilistic extrapolation framework}$ for data mixture optimization that avoids rigid assumptions and explicitly models the uncertainty in performance across decision variables. We formulate data curation as a sequential decision-making problem$\unicode{x2013}$multi-fidelity, multi-scale Bayesian optimization$\unicode{x2013}$where $\{$data mixtures, model scale, training steps$\}$ are adaptively selected to balance training cost and potential information gain. Our framework naturally gives rise to algorithm prototypes that leverage noisy information from inexpensive experiments to systematically inform costly training decisions. To accelerate methodological progress, we build a simulator based on 472 language model pre-training runs with varying data compositions from the SlimPajama dataset. We observe that even simple kernels and acquisition functions can enable principled decisions across training models from 20M to 1B parameters and achieve $\textbf{2.6x}$ and $\textbf{3.3x}$ speedups compared to multi-fidelity BO and random search baselines. Taken together, our framework underscores potential efficiency gains achievable by developing principled and transferable data mixture optimization methods.

Tianyi Peng, George Gui, Daniel J. Merlau et al.

Digital representations of individuals ("digital twins") promise to transform social science and decision-making. Yet it remains unclear whether such twins truly mirror the people they emulate. We conducted 19 preregistered studies with a representative U.S. panel and their digital twins, each constructed from rich individual-level data, enabling direct comparisons between human and twin behavior across a wide range of domains and stimuli (including never-seen-before ones). Twins reproduced individual responses with 75% accuracy and seemingly low correlation with human answers (approximately 0.2). However, this apparently high accuracy was no higher than that achieved by generic personas based on demographics only. In contrast, correlation improved when twins incorporated detailed personal information, even outperforming traditional machine learning benchmarks that require additional data. Twins exhibited systematic strengths and weaknesses - performing better in social and personality domains, but worse in political ones - and were more accurate for participants with higher education, higher income, and moderate political views and religious attendance. Together, these findings delineate both the promise and the current limits of digital twins: they capture some relative differences among individuals but not yet the unique judgments of specific people. All data and code are publicly available to support the further development and evaluation of digital twin pipelines.

Naimeng Ye, Xiao Yu, Ruize Xu et al.

Automated web testing plays a critical role in ensuring high-quality user experiences and delivering business value. Traditional approaches primarily focus on code coverage and load testing, but often fall short of capturing complex user behaviors, leaving many usability issues undetected. The emergence of large language models (LLM) and AI agents opens new possibilities for web testing by enabling human-like interaction with websites and a general awareness of common usability problems. In this work, we present WebProber, a prototype AI agent-based web testing framework. Given a URL, WebProber autonomously explores the website, simulating real user interactions, identifying bugs and usability issues, and producing a human-readable report. We evaluate WebProber through a case study of 120 academic personal websites, where it uncovered 29 usability issues--many of which were missed by traditional tools. Our findings highlight agent-based testing as a promising direction while outlining directions for developing next-generation, user-centered testing frameworks.

Shuze Chen, Tianyi Peng

Value decomposition has long been a fundamental technique in multi-agent dynamic programming and reinforcement learning (RL). Specifically, the value function of a global state $(s_1,s_2,\ldots,s_N)$ is often approximated as the sum of local functions: $V(s_1,s_2,\ldots,s_N)\approx\sum_{i=1}^N V_i(s_i)$. This approach traces back to the index policy in restless multi-armed bandit problems and has found various applications in modern RL systems. However, the theoretical justification for why this decomposition works so effectively remains underexplored. In this paper, we uncover the underlying mathematical structure that enables value decomposition. We demonstrate that a multi-agent Markov decision process (MDP) permits value decomposition if and only if its transition matrix is not "entangled" -- a concept analogous to quantum entanglement in quantum physics. Drawing inspiration from how physicists measure quantum entanglement, we introduce how to measure the "Markov entanglement" for multi-agent MDPs and show that this measure can be used to bound the decomposition error in general multi-agent MDPs. Using the concept of Markov entanglement, we proved that a widely-used class of index policies is weakly entangled and enjoys a sublinear $\mathcal O(\sqrt{N})$ scale of decomposition error for $N$-agent systems. Finally, we show how Markov entanglement can be efficiently estimated in practice, providing practitioners with an empirical proxy for the quality of value decomposition.

Vivek Farias, Joren Gijsbrechts, Aryan Khojandi et al.

Simulating a single trajectory of a dynamical system under some state-dependent policy is a core bottleneck in policy optimization (PO) algorithms. The many inherently serial policy evaluations that must be performed in a single simulation constitute the bulk of this bottleneck. In applying PO to supply chain optimization (SCO) problems, simulating a single sample path corresponding to one month of a supply chain can take several hours. We present an iterative algorithm to accelerate policy simulation, dubbed Picard Iteration. This scheme carefully assigns policy evaluation tasks to independent processes. Within an iteration, any given process evaluates the policy only on its assigned tasks while assuming a certain "cached" evaluation for other tasks; the cache is updated at the end of the iteration. Implemented on GPUs, this scheme admits batched evaluation of the policy across a single trajectory. We prove that the structure afforded by many SCO problems allows convergence in a small number of iterations independent of the horizon. We demonstrate practical speedups of 400x on large-scale SCO problems even with a single GPU, and also demonstrate practical efficacy in other RL environments.

Vivek F. Farias, Hao Li, Tianyi Peng et al.

Interference is a ubiquitous problem in experiments conducted on two-sided content marketplaces, such as Douyin (China's analog of TikTok). In many cases, creators are the natural unit of experimentation, but creators interfere with each other through competition for viewers' limited time and attention. "Naive" estimators currently used in practice simply ignore the interference, but in doing so incur bias on the order of the treatment effect. We formalize the problem of inference in such experiments as one of policy evaluation. Off-policy estimators, while unbiased, are impractically high variance. We introduce a novel Monte-Carlo estimator, based on "Differences-in-Qs" (DQ) techniques, which achieves bias that is second-order in the treatment effect, while remaining sample-efficient to estimate. On the theoretical side, our contribution is to develop a generalized theory of Taylor expansions for policy evaluation, which extends DQ theory to all major MDP formulations. On the practical side, we implement our estimator on Douyin's experimentation platform, and in the process develop DQ into a truly "plug-and-play" estimator for interference in real-world settings: one which provides robust, low-bias, low-variance treatment effect estimates; admits computationally cheap, asymptotically exact uncertainty quantification; and reduces MSE by 99\% compared to the best existing alternatives in our applications.

Vivek Farias, Ciamac Moallemi, Tianyi Peng et al.

This paper presents a new dynamic approach to experiment design in settings where, due to interference or other concerns, experimental units are coarse. `Region-split' experiments on online platforms are one example of such a setting. The cost, or regret, of experimentation is a natural concern here. Our new design, dubbed Synthetically Controlled Thompson Sampling (SCTS), minimizes the regret associated with experimentation at no practically meaningful loss to inferential ability. We provide theoretical guarantees characterizing the near-optimal regret of our approach, and the error rates achieved by the corresponding treatment effect estimator. Experiments on synthetic and real world data highlight the merits of our approach relative to both fixed and `switchback' designs common to such experimental settings.

Vivek F. Farias, Andrew A. Li, Tianyi Peng

The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and data collected from web-commerce systems such as recommendation engines. An important unresolved question for this problem is characterizing the distribution of estimated matrix entries under common low-rank estimators. Such a characterization is essential to any application that requires quantification of uncertainty in these estimates and has heretofore only been available under the assumption of homogenous Gaussian noise. Here we characterize the distribution of estimated matrix entries when the observation noise is heterogeneous sub-exponential and provide, as an application, explicit formulas for this distribution when observed entries are Poisson or Binary distributed.

Vivek F. Farias, Andrew A. Li, Tianyi Peng

The problem of causal inference with panel data is a central econometric question. The following is a fundamental version of this problem: Let $M^*$ be a low rank matrix and $E$ be a zero-mean noise matrix. For a `treatment' matrix $Z$ with entries in $\{0,1\}$ we observe the matrix $O$ with entries $O_{ij} := M^*_{ij} + E_{ij} + \mathcal{T}_{ij} Z_{ij}$ where $\mathcal{T}_{ij} $ are unknown, heterogenous treatment effects. The problem requires we estimate the average treatment effect $τ^* := \sum_{ij} \mathcal{T}_{ij} Z_{ij} / \sum_{ij} Z_{ij}$. The synthetic control paradigm provides an approach to estimating $τ^*$ when $Z$ places support on a single row. This paper extends that framework to allow rate-optimal recovery of $τ^*$ for general $Z$, thus broadly expanding its applicability. Our guarantees are the first of their type in this general setting. Computational experiments on synthetic and real-world data show a substantial advantage over competing estimators.

Vivek F. Farias, Andrew A. Li, Tianyi Peng

Inaccurate records of inventory occur frequently, and by some measures cost retailers approximately 4% in annual sales. Detecting inventory inaccuracies manually is cost-prohibitive, and existing algorithmic solutions rely almost exclusively on learning from longitudinal data, which is insufficient in the dynamic environment induced by modern retail operations. Instead, we propose a solution based on cross-sectional data over stores and SKUs, observing that detecting inventory inaccuracies can be viewed as a problem of identifying anomalies in a (low-rank) Poisson matrix. State-of-the-art approaches to anomaly detection in low-rank matrices apparently fall short. Specifically, from a theoretical perspective, recovery guarantees for these approaches require that non-anomalous entries be observed with vanishingly small noise (which is not the case in our problem, and indeed in many applications). So motivated, we propose a conceptually simple entry-wise approach to anomaly detection in low-rank Poisson matrices. Our approach accommodates a general class of probabilistic anomaly models. We show that the cost incurred by our algorithm approaches that of an optimal algorithm at a min-max optimal rate. Using synthetic data and real data from a consumer goods retailer, we show that our approach provides up to a 10x cost reduction over incumbent approaches to anomaly detection. Along the way, we build on recent work that seeks entry-wise error guarantees for matrix completion, establishing such guarantees for sub-exponential matrices, a result of independent interest.

Jackie Baek, Vivek F. Farias, Andreea Georgescu et al.

This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models, including the Bass model (used in modeling consumer adoption) and the SIR model (used in modeling epidemics). We show that one cannot hope to learn such models until quite late in the diffusion. Specifically, we show that the time required to collect a number of observations that exceeds our sample complexity lower bounds is large. For Bass models with low innovation rates, our results imply that one cannot hope to predict the eventual number of adopting customers until one is at least two-thirds of the way to the time at which the rate of new adopters is at its peak. In a similar vein, our results imply that in the case of an SIR model, one cannot hope to predict the eventual number of infections until one is approximately two-thirds of the way to the time at which the infection rate has peaked. This lower bound in estimation further translates into a lower bound in regret for decision-making in epidemic interventions. Our results formalize the challenge of accurate forecasting and highlight the importance of incorporating additional data sources. To this end, we analyze the benefit of a seroprevalence study in an epidemic, where we characterize the size of the study needed to improve SIR model estimation. Extensive empirical analyses on product adoption and epidemic data support our theoretical findings.