arXiv subjects

Danica J. Sutherland

Publications and source records attributed to Danica J. Sutherland.

At least 19 recordsLinked to original sources

arXiv2026

Conditional Independence Is Not (Quite) Pointwise Testable

Shah and Peters showed that a conditional independence test with finite-sample or uniformly-controlled level has only trivial power against any alternative. Most practical tests, however, only claim pointwise asymptotic level. There have been incorrect claims in the literature of conditional independence tests with pointwise asymptotic level and consistency against any alternative; whether such a test actually exists has remained open. We resolve this question. Even restricting to hypotheses with a bounded density on compact subsets of Euclidean spaces, for any sequence of (possibly randomized) tests with pointwise asymptotic level $α$, for every $\varepsilon > 0$ there is a conditionally dependent distribution where the test's limsup power is at most $α+ \varepsilon$. This remains true when the level control is required only over conditionally independent distributions with a continuous density and a uniformly continuous conditional law, and the conditionally dependent distributions have smooth densities. On the other hand, the extreme limitation of trivial power against any alternative for uniform-level tests does not apply to tests with pointwise level. We exhibit a test that, without regularity assumptions, has pointwise asymptotic level $α$, strictly higher power for all alternatives, and power tending to one for all distributions whose dependence exceeds a chosen scalar threshold.

math.ST↗

arXiv2026

Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.

stat.ML↗

arXiv2026

Maximum Mean Discrepancy with Unequal Sample Sizes via Generalized U-Statistics

Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require discarding valuable data, unnecessarily reducing test power. We address this long-standing limitation by extending the theory of generalized U-statistics and applying it to the usual MMD estimator, resulting in new characterization of the asymptotic distributions of the MMD estimator with unequal sample sizes (particularly outside the proportional regimes required by previous partial results). This generalization also provides a new criterion for optimizing the power of an MMD test with unequal sample sizes. Our approach preserves all available data, enhancing test accuracy and applicability in realistic settings. Along the way, we give much cleaner characterizations of the variance of MMD estimators, revealing something that might be surprising to those in the area: while zero MMD implies a degenerate estimator, it is sometimes possible to have a degenerate estimator with nonzero MMD as well; we give a construction and a proof that it does not happen in common situations.

stat.ML↗

arXiv2026

SeedER: Seed-and-Expand Retrieval from Knowledge Graphs

Knowledge graphs (KGs) offer a rich representation for relational knowledge, but their irregular structure makes retrieval challenging: ego-graph expansion grows rapidly, and dense embedding methods struggle with multi-hop compositional queries. Existing agent-based graph exploration approaches, while expressive, are often too expensive for large-scale retrieval. We introduce SeedER (Seed-and-Expand Retrieval), a retrieval framework that explicitly leverages KG structure through iterative, low-cost expansion. SeedER first seeds a compact set of core nodes using lightweight dense and entity-based retrieval, then selectively expands this set via a learned graph-aware policy trained with reinforcement learning. This design decomposes global reasoning into reusable local decisions, enabling efficient discovery of query-relevant nodes while tightly controlling expansion cost. We show theoretical limitations of dense retrieval on compositional graph queries, and establish advantages of SeedER from both compositional generalization and graph-constrained submodular optimization perspectives. Empirically, SeedER substantially improves recall with compact candidate sets over strong dense and graph-augmented baselines, making it an effective first-stage retriever for knowledge-intensive reasoning systems.

cs.LG↗

arXiv2026

Learning Representations for Independence Testing

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any dependence with enough samples, standard tests may require an exorbitant amount of samples for detecting subtle dependencies between high-dimensional random variables with complex distributions. In this work, we study two related ways to learn powerful independence tests. First, we show how to construct powerful statistical tests with finite-sample validity by using variational estimators of mutual information, such as the InfoNCE or NWJ estimators. Second, we establish a close connection between these variational mutual information-based tests and tests based on the Hilbert-Schmidt Independence Criterion (HSIC); in particular, learning a variational bound (typically parameterized by a deep network) for mutual information is closely related to learning a kernel for HSIC. Finally, we show how to, rather than selecting a representation to maximize the statistic itself, select a representation which can maximize the power of a test, in either setting; we term the former case a Neural Dependency Statistic (NDS). While HSIC power optimization has been recently considered in the literature, we correct some important misconceptions and expand to considering deep kernels. In our experiments, while all approaches can yield powerful tests with exact level control, optimized HSIC tests generally outperform the other approaches on difficult problems of detecting structured dependence.

stat.ML↗

arXiv2026

Token Hidden Reward: Steering Exploration-Exploitation in Group Relative Deep Reinforcement Learning

Reinforcement learning with verifiable rewards has significantly advanced the reasoning capabilities of large language models, yet how to explicitly steer training toward exploration or exploitation remains an open problem. We introduce Token Hidden Reward (THR), a token-level metric that quantifies each token's influence on the likelihood of correct responses under Group Relative Policy Optimization (GRPO). We find that training dynamics are dominated by a small subset of tokens with high absolute THR values. Most interestingly, tokens with positive THR strengthen confidence in correct outputs, thus favoring exploitation, while tokens with negative THR preserve probability mass for alternative outputs, enabling exploration. This insight suggests a natural intervention: a THR-guided reweighting algorithm that modulates GRPO's learning signals to explicitly bias training toward exploitation or exploration. We validate the efficacy of this algorithm on diverse math reasoning benchmarks. By amplifying tokens with positive THR value and weakening negative ones, our algorithm improves greedy-decoding accuracy, favoring exploitation. The reverse strategy yields consistent gains in Pass@K accuracy, favoring exploration. We further demonstrate that our algorithm integrates seamlessly with other RL objectives such as GSPO and generalizes across architectures including Llama. These findings establish THR as a principled and fine-grained mechanism for dynamically controlling exploration and exploitation in RL-tuned LLMs, providing new tools for targeted fine-tuning in reasoning-intensive applications.

cs.LG↗

arXiv2025

On the Hardness of Conditional Independence Testing In Practice

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test - of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case - and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type-I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type-I error.

stat.ML↗

arXiv2025

Diffusion-Driven Two-Stage Active Learning for Low-Budget Semantic Segmentation

Semantic segmentation demands dense pixel-level annotations, which can be prohibitively expensive - especially under extremely constrained labeling budgets. In this paper, we address the problem of low-budget active learning for semantic segmentation by proposing a novel two-stage selection pipeline. Our approach leverages a pre-trained diffusion model to extract rich multi-scale features that capture both global structure and fine details. In the first stage, we perform a hierarchical, representation-based candidate selection by first choosing a small subset of representative pixels per image using MaxHerding, and then refining these into a diverse global pool. In the second stage, we compute an entropy-augmented disagreement score (eDALD) over noisy multi-scale diffusion features to capture both epistemic uncertainty and prediction confidence, selecting the most informative pixels for annotation. This decoupling of diversity and uncertainty lets us achieve high segmentation accuracy with only a tiny fraction of labeled pixels. Extensive experiments on four benchmarks (CamVid, ADE-Bed, Cityscapes, and Pascal-Context) demonstrate that our method significantly outperforms existing baselines under extreme pixel-budget regimes. Our code is available at https://github.com/jn-kim/two-stage-edald.

cs.CV↗

arXiv2025

DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing

To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly maximizing multiple kernel-based statistics may result in highly similar kernels that capture highly overlapping information, limiting the effectiveness of aggregation. To address this, we propose an aggregated statistic that explicitly incorporates kernel diversity based on the covariance between different kernels. Moreover, we identify a fundamental challenge: a trade-off between the diversity among kernels and the test power of individual kernels, i.e., the selected kernels should be both effective and diverse. This motivates a testing framework with selection inference, which leverages information from the training phase to select kernels with strong individual performance from the learned diverse kernel pool. We provide rigorous theoretical statements and proofs to show the consistency on the test power and control of Type-I error, along with asymptotic analysis of the proposed statistics. Lastly, we conducted extensive empirical experiments demonstrating the superior performance of our proposed approach across various benchmarks for both two-sample and independence testing.

cs.LG↗

arXiv2025

Practical Kernel Tests of Conditional Independence

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of false positives), while still attaining competitive test power. Excess false positives arise due to bias in the test statistic, which is in our case obtained using nonparametric kernel ridge regression. We propose SplitKCI, an automated method for bias control for the Kernel-based Conditional Independence (KCI) test based on data splitting. We show that our approach significantly improves test level control for KCI without sacrificing test power, both theoretically and for synthetic and real-world data.

cs.LG↗

arXiv2025

Learning Dynamics of LLM Finetuning

Learning dynamics, which describes how the learning of specific training examples influences the model's predictions on other examples, gives us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during different types of finetuning, by analyzing the step-wise decomposition of how influence accumulates among different potential responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. In particular, we propose a hypothetical explanation of why specific types of hallucination are strengthened after finetuning, e.g., the model might use phrases or facts in the response for question B to answer question A, or the model might keep repeating similar simple phrases when generating responses. We also extend our framework and highlight a unique "squeezing effect" to explain a previously observed phenomenon in off-policy direct preference optimization (DPO), where running DPO for too long makes even the desired outputs less likely. This framework also provides insights into where the benefits of on-policy DPO and other variants come from. The analysis not only provides a novel perspective of understanding LLM's finetuning but also inspires a simple, effective method to improve alignment performance.

cs.LG↗

arXiv2025

Efficient kernelized bandit algorithms via exploration distributions

We consider a kernelized bandit problem with a compact arm set ${X} \subset \mathbb{R}^d $ and a fixed but unknown reward function $f^*$ with a finite norm in some Reproducing Kernel Hilbert Space (RKHS). We propose a class of computationally efficient kernelized bandit algorithms, which we call GP-Generic, based on a novel concept: exploration distributions. This class of algorithms includes Upper Confidence Bound-based approaches as a special case, but also allows for a variety of randomized algorithms. With careful choice of exploration distribution, our proposed generic algorithm realizes a wide range of concrete algorithms that achieve $\tilde{O}(γ_T\sqrt{T})$ regret bounds, where $γ_T$ characterizes the RKHS complexity. This matches known results for UCB- and Thompson Sampling-based algorithms; we also show that in practice, randomization can yield better practical results.

cs.LG↗

arXiv2025

On the Effect of Negative Gradient in Group Relative Deep Reinforcement Optimization

Reinforcement learning (RL) has become popular in enhancing the reasoning capabilities of large language models (LLMs), with Group Relative Policy Optimization (GRPO) emerging as a widely used algorithm in recent systems. Despite GRPO's widespread adoption, we identify a previously unrecognized phenomenon we term Lazy Likelihood Displacement (LLD), wherein the likelihood of correct responses marginally increases or even decreases during training. This behavior mirrors a recently discovered misalignment issue in Direct Preference Optimization (DPO), attributed to the influence of negative gradients. We provide a theoretical analysis of GRPO's learning dynamic, identifying the source of LLD as the naive penalization of all tokens in incorrect responses with the same strength. To address this, we develop a method called NTHR, which downweights penalties on tokens contributing to the LLD. Unlike prior DPO-based approaches, NTHR takes advantage of GRPO's group-based structure, using correct responses as anchors to identify influential tokens. Experiments on math reasoning benchmarks demonstrate that NTHR effectively mitigates LLD, yielding consistent performance gains across models ranging from 0.5B to 3B parameters.

cs.LG↗

arXiv2025

Uncertainty Herding: One Active Learning Method for All Label Budgets

Most active learning research has focused on methods which perform well when many labels are available, but can be dramatically worse than random selection when label budgets are small. Other methods have focused on the low-budget regime, but do poorly as label budgets increase. As the line between "low" and "high" budgets varies by problem, this is a serious issue in practice. We propose uncertainty coverage, an objective which generalizes a variety of low- and high-budget objectives, as well as natural, hyperparameter-light methods to smoothly interpolate between low- and high-budget regimes. We call greedy optimization of the estimate Uncertainty Herding; this simple method is computationally fast, and we prove that it nearly optimizes the distribution-level coverage. In experimental validation across a variety of active learning tasks, our proposal matches or beats state-of-the-art performance in essentially all cases; it is the only method of which we are aware that reliably works well in both low- and high-budget settings.

cs.LG↗

arXiv2024

Bias Amplification in Language Model Evolution: An Iterated Learning Perspective

With the widespread adoption of Large Language Models (LLMs), the prevalence of iterative interactions among these models is anticipated to increase. Notably, recent advancements in multi-round self-improving methods allow LLMs to generate new examples for training subsequent models. At the same time, multi-agent LLM systems, involving automated interactions among agents, are also increasing in prominence. Thus, in both short and long terms, LLMs may actively engage in an evolutionary process. We draw parallels between the behavior of LLMs and the evolution of human culture, as the latter has been extensively studied by cognitive scientists for decades. Our approach involves leveraging Iterated Learning (IL), a Bayesian framework that elucidates how subtle biases are magnified during human cultural evolution, to explain some behaviors of LLMs. This paper outlines key characteristics of agents' behavior in the Bayesian-IL framework, including predictions that are supported by experimental verification with various LLMs. This theoretical framework could help to more effectively predict and guide the evolution of LLMs in desired directions.

cs.CL↗

arXiv2024

Understanding Simplicity Bias towards Compositional Mappings via Learning Dynamics

Obtaining compositional mappings is important for the model to generalize well compositionally. To better understand when and how to encourage the model to learn such mappings, we study their uniqueness through different perspectives. Specifically, we first show that the compositional mappings are the simplest bijections through the lens of coding length (i.e., an upper bound of their Kolmogorov complexity). This property explains why models having such mappings can generalize well. We further show that the simplicity bias is usually an intrinsic property of neural network training via gradient descent. That partially explains why some models spontaneously generalize well when they are trained appropriately.

cs.LG↗

arXiv2024

Exploring Active Learning in Meta-Learning: Enhancing Context Set Labeling

Most meta-learning methods assume that the (very small) context set used to establish a new task at test time is passively provided. In some settings, however, it is feasible to actively select which points to label; the potential gain from a careful choice is substantial, but the setting requires major differences from typical active learning setups. We clarify the ways in which active meta-learning can be used to label a context set, depending on which parts of the meta-learning process use active learning. Within this framework, we propose a natural algorithm based on fitting Gaussian mixtures for selecting which points to label; though simple, the algorithm also has theoretical motivation. The proposed algorithm outperforms state-of-the-art active learning methods when used with various meta-learning algorithms across several benchmark datasets.

cs.LG↗

arXiv2024

Generalized Coverage for More Robust Low-Budget Active Learning

The ProbCover method of Yehuda et al. is a well-motivated algorithm for active learning in low-budget regimes, which attempts to "cover" the data distribution with balls of a given radius at selected data points. We demonstrate, however, that the performance of this algorithm is extremely sensitive to the choice of this radius hyper-parameter, and that tuning it is quite difficult, with the original heuristic frequently failing. We thus introduce (and theoretically motivate) a generalized notion of "coverage," including ProbCover's objective as a special case, but also allowing smoother notions that are far more robust to hyper-parameter choice. We propose an efficient greedy method to optimize this coverage, generalizing ProbCover's algorithm; due to its close connection to kernel herding, we call it "MaxHerding." The objective can also be optimized non-greedily through a variant of $k$-medoids, clarifying the relationship to other low-budget active learning methods. In comprehensive experiments, MaxHerding surpasses existing active learning methods across multiple low-budget image classification benchmarks, and does so with less computational cost than most competitive methods.

cs.LG↗