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Song Wei

Publications and source records attributed to Song Wei.

18 recordsLinked to original sources
arXiv2026

Algorithmic Contract Design at Scale: Adaptive Peer Comparison for Enterprise Pricing

In enterprise software, a contract commits the customer to a usage volume over a fixed term in exchange for discounted pricing. These contracts are individually negotiated across many dimensions -- size, duration, industry, product mix, usage history -- and without a data-driven reference point, discounts tend to be overly generous. Manual governance review enforces discipline but at days-scale per contract, with inconsistency across reviewers and no real-time feedback to sellers. We present \emph{Contract Scoring}, a peer-based grading system deployed on every contract at Databricks. The system identifies empirically similar historical contracts via adaptive nearest neighbors over ensemble trees, where shared leaf membership defines a data-driven similarity learned from the discount target. It returns a letter grade with per-product-line breakdown in seconds; the underlying peer set is available to the centralized review team for audit. Sellers treat the grade as a contract design ``exit criterion'', iteratively adjusting discount structures until the grade reflects their intended tradeoff. Deployment evidence shows measurable discount discipline across the scored portfolio, with a commercially significant impact on revenue.

stat.AP↗
arXiv2026

Bias-Aware Confidence Intervals for Synthetic Control via Placebo-in-Time Bootstrap

Synthetic control (SC) methods are among the most widely used tools for causal inference without randomization. The standard Gaussian confidence interval around the estimated effect is simple, fast, and reliably directional when the treatment signal is strong, so practitioners default to it for good reason. Most treated populations, however, are bottom-heavy in intensity, and for them the SC model's systematic bias rivals or exceeds the signal even under good pre-treatment fit. Because this bias shares sign across units it does not average out, and the Gaussian confidence interval shrinks past it and converges on a wrong center. The failure is not imprecision but misdirection: a positive effect estimated as negligible is a missed opportunity, while a negligible effect estimated as significantly positive leads to continued investment in an intervention that is not working. No existing confidence interval for the SC effect measures this bias. We propose a placebo-in-time bootstrap that estimates the bias distribution directly from the observed panel. For each treated unit the procedure backdates the treatment onset and refits the SC model at each placebo onset; the resulting placebo gaps are draws from the same bias distribution that contaminates the real estimate, and bootstrapping them yields a critical value calibrated at the zero null. Because the method resamples realized model error rather than a hypothesized effect, coverage is trajectory-agnostic: it holds at fixed width regardless of how the true effect evolves over time.

stat.ME↗
arXiv2026

More Skills, Worse Agents? Skill Shadowing Degrades Performance When Expanding Skill Libraries

Skill libraries allow LLM agents to load task-specific instructions on demand, letting non-expert users solve domain-specific tasks through natural language without knowing which skills exist or how they work. However, performance degrades as libraries grow -- by up to 21\% when scaling from a small set of helpful skills to a 202-skill library. In this work, we formulate this performance degradation as the pass rate drop between loading a library of known-helpful skills and the full library. Moreover, we propose to decompose the pass rate drop by conditioning on the skill(s) invocation -- which skills the agent selects during a trajectory -- into two effects: \emph{skill shadowing}, where the agent selects wrong skills more often as the library expands, and \emph{context overhead}, where the enlarged context degrades execution even when selection is correct. We derive upper bounds on both effects to characterize their magnitudes of impacts to the pass rate drop. Our empirical estimates of the effects and their upper bounds both show that the \emph{skill shadowing} effect grows with library size and significantly contributes to the performance degradation, whereas the \emph{context overhead} effect remains small and indistinguishable from zero. This observed asymmetry establishes that the skill selection failure, not the enlarged context, is the primary bottleneck when expanding the skill libraries.

cs.SE↗
arXiv2023

Scene-Driven Multimodal Knowledge Graph Construction for Embodied AI

Embodied AI is one of the most popular studies in artificial intelligence and robotics, which can effectively improve the intelligence of real-world agents (i.e. robots) serving human beings. Scene knowledge is important for an agent to understand the surroundings and make correct decisions in the varied open world. Currently, knowledge base for embodied tasks is missing and most existing work use general knowledge base or pre-trained models to enhance the intelligence of an agent. For conventional knowledge base, it is sparse, insufficient in capacity and cost in data collection. For pre-trained models, they face the uncertainty of knowledge and hard maintenance. To overcome the challenges of scene knowledge, we propose a scene-driven multimodal knowledge graph (Scene-MMKG) construction method combining conventional knowledge engineering and large language models. A unified scene knowledge injection framework is introduced for knowledge representation. To evaluate the advantages of our proposed method, we instantiate Scene-MMKG considering typical indoor robotic functionalities (Manipulation and Mobility), named ManipMob-MMKG. Comparisons in characteristics indicate our instantiated ManipMob-MMKG has broad superiority in data-collection efficiency and knowledge quality. Experimental results on typical embodied tasks show that knowledge-enhanced methods using our instantiated ManipMob-MMKG can improve the performance obviously without re-designing model structures complexly. Our project can be found at https://sites.google.com/view/manipmob-mmkg

cs.AI↗
arXiv2023

Assessing Electricity Service Unfairness with Transfer Counterfactual Learning

Energy justice is a growing area of interest in interdisciplinary energy research. However, identifying systematic biases in the energy sector remains challenging due to confounding variables, intricate heterogeneity in counterfactual effects, and limited data availability. First, this paper demonstrates how one can evaluate counterfactual unfairness in a power system by analyzing the average causal effect of a specific protected attribute. Subsequently, we use subgroup analysis to handle model heterogeneity and introduce a novel method for estimating counterfactual unfairness based on transfer learning, which helps to alleviate the data scarcity in each subgroup. In our numerical analysis, we apply our method to a unique large-scale customer-level power outage data set and investigate the counterfactual effect of demographic factors, such as income and age of the population, on power outage durations. Our results indicate that low-income and elderly-populated areas consistently experience longer power outages under both daily and post-disaster operations, and such discrimination is exacerbated under severe conditions. These findings suggest a widespread, systematic issue of injustice in the power service systems and emphasize the necessity for focused interventions in disadvantaged communities.

cs.LG↗
arXiv2023

INTAGS: Interactive Agent-Guided Simulation

In many applications involving multi-agent system (MAS), it is imperative to test an experimental (Exp) autonomous agent in a high-fidelity simulator prior to its deployment to production, to avoid unexpected losses in the real-world. Such a simulator acts as the environmental background (BG) agent(s), called agent-based simulator (ABS), aiming to replicate the complex real MAS. However, developing realistic ABS remains challenging, mainly due to the sequential and dynamic nature of such systems. To fill this gap, we propose a metric to distinguish between real and synthetic multi-agent systems, which is evaluated through the live interaction between the Exp and BG agents to explicitly account for the systems' sequential nature. Specifically, we characterize the system/environment by studying the effect of a sequence of BG agents' responses to the environment state evolution and take such effects' differences as MAS distance metric; The effect estimation is cast as a causal inference problem since the environment evolution is confounded with the previous environment state. Importantly, we propose the Interactive Agent-Guided Simulation (INTAGS) framework to build a realistic ABS by optimizing over this novel metric. To adapt to any environment with interactive sequential decision making agents, INTAGS formulates the simulator as a stochastic policy in reinforcement learning. Moreover, INTAGS utilizes the policy gradient update to bypass differentiating the proposed metric such that it can support non-differentiable operations of multi-agent environments. Through extensive experiments, we demonstrate the effectiveness of INTAGS on an equity stock market simulation example. We show that using INTAGS to calibrate the simulator can generate more realistic market data compared to the state-of-the-art conditional Wasserstein Generative Adversarial Network approach.

cs.LG↗
arXiv2023

Transfer Learning for Causal Effect Estimation

We present a Transfer Causal Learning (TCL) framework when target and source domains share the same covariate/feature spaces, aiming to improve causal effect estimation accuracy in limited data. Limited data is very common in medical applications, where some rare medical conditions, such as sepsis, are of interest. Our proposed method, named \texttt{$\ell_1$-TCL}, incorporates $\ell_1$ regularized TL for nuisance models (e.g., propensity score model); the TL estimator of the nuisance parameters is plugged into downstream average causal/treatment effect estimators (e.g., inverse probability weighted estimator). We establish non-asymptotic recovery guarantees for the \texttt{$\ell_1$-TCL} with generalized linear model (GLM) under the sparsity assumption in the high-dimensional setting, and demonstrate the empirical benefits of \texttt{$\ell_1$-TCL} through extensive numerical simulation for GLM and recent neural network nuisance models. Our method is subsequently extended to real data and generates meaningful insights consistent with medical literature, a case where all baseline methods fail.

cs.LG↗
arXiv2023

Causal Graph Discovery from Self and Mutually Exciting Time Series

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.

cs.LG↗
arXiv2023

Causal Structural Learning from Time Series: A Convex Optimization Approach

Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization problem; however, DAG learning remains a highly non-convex problem, and there has not been much work on leveraging well-developed convex optimization techniques for causal structural learning. We fill this gap by proposing a data-adaptive linear approach for causal structural learning from time series data, which can be conveniently cast into a convex optimization problem using a recently developed monotone operator variational inequality (VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee of the VI-based approach and show the superior performance of our proposed method on structure recovery over existing methods via extensive numerical experiments.

cs.LG↗
arXiv2022

Online Kernel CUSUM for Change-Point Detection

We present a computationally efficient online kernel Cumulative Sum (CUSUM) method for change-point detection that utilizes the maximum over a set of kernel statistics to account for the unknown change-point location. Our approach exhibits increased sensitivity to small changes compared to existing kernel-based change-point detection methods, including Scan-B statistic, corresponding to a non-parametric Shewhart chart-type procedure. We provide accurate analytic approximations for two key performance metrics: the Average Run Length (ARL) and Expected Detection Delay (EDD), which enable us to establish an optimal window length to be on the order of the logarithm of ARL to ensure minimal power loss relative to an oracle procedure with infinite memory. Moreover, we introduce a recursive calculation procedure for detection statistics to ensure constant computational and memory complexity, which is essential for online implementation. Through extensive experiments on both simulated and real data, we demonstrate the competitive performance of our method and validate our theoretical results.

stat.ME↗
arXiv2022

Optimal Sub-sampling to Boost Power of Kernel Sequential Change-point Detection

We present a novel scheme to boost detection power for kernel maximum mean discrepancy based sequential change-point detection procedures. Our proposed scheme features an optimal sub-sampling of the history data before the detection procedure, in order to tackle the power loss incurred by the random sub-sample from the enormous history data. We apply our proposed scheme to both Scan $B$ and Kernel Cumulative Sum (CUSUM) procedures, and improved performance is observed from extensive numerical experiments.

stat.ME↗
arXiv2022

Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes

Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Clinically relevant and interpretable results require a framework that can (i) infer temporal interactions across multiple patient features found in EMR data (e.g., Labs, vital signs, etc.) and (ii) identify patterns that precede and are specific to an impending adverse event (e.g., sepsis). In this work, we propose a linear multivariate Hawkes process model, coupled with ReLU link function, to recover a Granger Causal (GC) graph with both exciting and inhibiting effects. We develop a scalable two-phase gradient-based method to obtain a maximum surrogate-likelihood estimator, which is shown to be effective via extensive numerical simulation. Our method is subsequently extended to a data set of patients admitted to Grady hospital system in Atlanta, GA, USA, where the estimated GC graph identifies several highly interpretable GC chains that precede sepsis. The code is available at \url{https://github.com/SongWei-GT/two-phase-MHP}.

stat.AP↗
arXiv2021

Causal Graph Discovery from Self and Mutually Exciting Time Series

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.

cs.LG↗
arXiv2021

Noisy Gradient Descent Converges to Flat Minima for Nonconvex Matrix Factorization

Numerous empirical evidences have corroborated the importance of noise in nonconvex optimization problems. The theory behind such empirical observations, however, is still largely unknown. This paper studies this fundamental problem through investigating the nonconvex rectangular matrix factorization problem, which has infinitely many global minima due to rotation and scaling invariance. Hence, gradient descent (GD) can converge to any optimum, depending on the initialization. In contrast, we show that a perturbed form of GD with an arbitrary initialization converges to a global optimum that is uniquely determined by the injected noise. Our result implies that the noise imposes implicit bias towards certain optima. Numerical experiments are provided to support our theory.

cs.LG↗
arXiv2021

Inferring serial correlation with dynamic backgrounds

Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a total variation constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The total variation constraint on the dynamic background encourages a piece-wise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano's method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.

math.ST↗
arXiv2020

Goodness-of-Fit Test for Mismatched Self-Exciting Processes

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test's good performance.

math.ST↗
arXiv2016

Fractional constitutive equation (FACE) for non-Newtonian fluid flow: Theoretical description

Non-Newtonian fluid flow might be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This short communication proposes a space FrActional-order Constitutive Equation (FACE) that links viscous shear stress with the velocity gradient, and then interprets physical properties of non-Newtonian fluids for steady pipe flow. Results show that the generalized FACE model contains previous non-Newtonian fluid flow models as end-members by simply adjusting the order of the fractional index, and a preliminary test shows that the FACE model conveniently captures the observed growth of shear stress for various velocity gradients. Further analysis of the velocity profile, frictional head loss, and Reynolds number using the FACE model also leads to analytical tools and criterion that can significantly extend standard models in quantifying the complex dynamics of non-Newtonian fluid flow with a wide range of spatially nonlocal velocities.

physics.flu-dyn↗
arXiv2013

A Matlab toolbox for fractional relaxation-oscillation equations

Stress relaxation and oscillation damping of complex viscoelastic media often manifest history- and path-dependent physical behaviors and cannot accurately be described by the classical models. Recent research found that fractional derivative models can characterize such complex relaxation and damping. However, to our best knowledge, easy-to-use numerical software is not available for fractional relaxation-oscillation (FRO) equations. This paper is to introduce an open source free Matlab toolbox which we developed in recent years for numerical solution of the FRO equations. This FRO toolbox uses the predictor-corrector approach for the discretization of time fractional derivative, and non-expert users can accurately solve fractional relaxation-oscillation equations via a friendly graphical user interface. Compared with experimental data, our numerical experiments show that the FRO toolbox is highly efficient and accurate to simulate viscoelastic stress relaxation and damped vibration. This free toolbox will help promote the research and practical use of fractional relaxation-oscillation equations.

math-ph↗