ICML 2026 论文列表

International Conference on Machine Learning

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Gradient-Aware Scheduling: Coupling Curriculum and Staleness for Async Reinforcement Learning

Xinyu Zhang

展开摘要

Asynchronous reinforcement learning (RL) accelerates LLM training through parallel data collection, but introduces *policy lag*: experiences are collected under stale policy weights, which destabilizes learning—especially on hard tasks. We identify why: **gradient variance scales exponentially with task difficulty under staleness**, because hard tasks have narrow solution spaces corresponding to sharp loss-landscape curvature (high Hessian eigenvalues). We formalize this as a *staleness budget optimization problem* and prove that the optimal allocation follows an exponential decay: $\eta^*(d) = \eta_{\text{base}} \cdot e^{-\lambda d}$ where $\lambda = \alpha/2$ is half the Hessian growth rate. Building on this principle, we propose **GAS (Gradient-Aware Scheduling)**, a drop-in recipe for fast and stable asynchronous RL with three components: (i) a bandit-based curriculum that selects task difficulty by learning signal (ACB); (ii) execution-aware staleness budgets that keep slow tasks from bottlenecking rollout (EAAS); and (iii) curriculum–staleness coupling that tightens the staleness budget as difficulty rises (CSC). Our mechanistic analysis validates the theoretical predictions: the "safe zone" of gradient coherence follows the derived exponential boundary. On code generation benchmarks, GAS improves Pass@1 from 39.7% to 60.1% while training at $2.3\times$ the throughput of synchronous GRPO, showing that matching each task's staleness budget to its difficulty (and thus to its loss-landscape curvature) makes asynchronous RL both fast and stable.

Poster
Class-Prior Perturbation-Robust Regularization for Imbalanced Unreliable Partial Label Learning

Congyu Qiao, Haohao Dong, Xin Geng, Ning Xu

展开摘要

Imbalanced Unreliable Partial Label Learning (I-UPLL) is a challenging weakly supervised learning setting in which severe class imbalance and unreliable candidate labels jointly degrade model performance. By revisiting existing approaches for imbalanced learning, we observe that most of them fundamentally rely on estimating the class prior to guide balancing operations, such as re-sampling, pseudo-label generation, or logit adjustment. However, under I-UPLL, obtaining stable and accurate prior estimates at the early stage of training is often unrealistic due to the ambiguity and unreliability of partial labels, thereby leading the model to rapidly converge to a suboptimal solution. To address this issue, we propose CLAPOR, a novel CLAss-PriOr perturbation-Robust regularization framework that fundamentally avoids dependence on accurate prior estimation. Specifically, the proposed regularization trains the model under deliberately perturbed class priors, sampled from a Dirichlet distribution that deviates from the current estimated prior. This design encourages consistent performance under prior uncertainty and naturally preserves attention to minority classes. Extensive experiments on benchmark datasets demonstrate the effectiveness of CLAPOR across various settings of I-UPLL.

Poster
LLMs Lean on Priors, Not Programming Language Semantics

Aditya Thimmaiah, Jiyang Zhang, Jayanth Srinivasa, Junyi Jessy Li, Milos Gligoric

展开摘要

Recent work asks whether large language models (LLMs) condition their reasoning on explicit rules rather than statistical regularities from pretraining. Program execution provides a canonical instance: formal semantics define behavior through symbolic transition rules that can be systematically altered under distribution shift. We investigate whether LLMs can condition their reasoning on formal semantics through program execution and introduce PLSemanticsBench, pairing featherweight C programs with two semantic systems—small-step operational semantics and K semantics—and probing four capabilities: composing rules for final states, selecting rules when state is unmutated, sustaining such conditioning over long traces, and following supplied rules under novel semantics. To decouple semantic reasoning from syntactic familiarity, we redefine familiar operators to induce symbol-meaning conflict and introduce novel symbols defined only through the supplied rules, and stress-test models on Human-Written, LLM-Translated, and Fuzzer-Generated splits with increasing structural complexity. Across 11 frontier LLMs, strong final-state accuracy under standard semantics (up to 90%) drops sharply—by as much as 40–60% points—under semantic mutations and increasing structural complexity. Only a handful of models achieve non-zero long-horizon conditioning accuracy, and even the best systems reach just 35%. Together, these results suggest that contemporary LLMs often rely on pretrained lexical associations rather than systematically conditioning on supplied formal rules. PLSemanticsBench is publicly available at https://EngineeringSoftware.github.io/PLSemanticsBench.

Poster
STARCaster: Spatio-Temporal AutoRegressive Video Diffusion for Identity- and View-Aware Talking Portraits

Foivos Paraperas Papantoniou, Stathis Galanakis, Rolandos Alexandros Potamias, Bernhard Kainz, Stefanos Zafeiriou

展开摘要

This paper presents STARCaster, an identity-aware spatio-temporal video diffusion model that addresses both speech-driven portrait animation and dynamic viewpoint control, given an identity embedding or reference image, within a unified framework. Existing 2D speech-to-video diffusion models depend heavily on reference guidance, leading to limited motion diversity. At the same time, 3D-aware animation typically relies on inversion through pretrained tri-plane generators, which often leads to imperfect reconstructions and identity drift. We rethink reference- and geometry-based paradigms in two ways. First, we deviate from strict reference conditioning at pretraining by introducing softer identity constraints. Second, we address 3D awareness implicitly within the 2D video domain by leveraging the inherent multi-view nature of video data. STARCaster adopts a compositional approach progressing from ID-aware motion modeling, to audio-visual synchronization via lip reading-based supervision, and finally to novel view animation through temporal-to-spatial adaptation. To overcome the scarcity of 4D audio-visual data, we propose a decoupled learning approach in which view consistency and temporal coherence are trained independently. Comprehensive evaluations demonstrate that STARCaster generalizes effectively across tasks and identities, consistently surpassing prior approaches in different benchmarks.

Poster
Information-Theoretic Generalization Bounds for VAEs: A Role of Encoder and Latent Variable

Futoshi Futami, Masahiro Fujisawa

展开摘要

Despite their remarkable success, a rigorous theoretical understanding of how latent variables (LVs) govern the generalization performance of Variational Autoencoders (VAEs) remains largely elusive. Existing theoretical analyses are confined to supervised learning or models with discrete latent spaces, leaving their role in standard VAEs with continuous LVs poorly understood. This paper establishes the first information-theoretic analysis for VAEs by adapting a theoretical framework from supervised learning---the leave-one-out conditional mutual information framework---to the unsupervised, continuous latent space of these models. Our analysis reveals that their generalization error is bounded solely by the information complexity of the encoder and LVs, independent of the decoder. The versatility of our framework is demonstrated through its extension to both hierarchical VAEs, for which we provide layer-wise bounds, and data generation, where we link our information-theoretic principles to a novel bound on the 2-Wasserstein distance between true and generated distributions.

Poster
The Geometry of Updates: Fisher Alignment at Vocabulary Scale

John Sweeney

展开摘要

Training-free source selection for LLM families with shared vocabularies arises in scientific string domains such as SMILES, protein, and genomic sequences, where candidate corpora share a tokenizer but differ in prediction targets. This creates an activation-dark regime: representation-similarity metrics can be uninformative without assumptions about label-conditioned error geometry, while classical update-geometry metrics are computationally prohibitive at vocabulary scale. We show that, in a shared-output head setting, representation metrics (e.g., CKA) are non-identifiable for transfer; models can share identical representations yet have orthogonal head updates. The key identity is that head Fisher alignment is exactly a cosine between kernel mean embeddings in the joint activation-error space, exposing activation, error, and coupling factors rather than requiring a materialized Fisher matrix. FisherSketch estimates this cosine directly in a single streaming pass, making K=128,256 head Fisher alignment practical with a 16 KB task signature (m=4096) and a 192 KB per-task streaming state–small enough to store next to a model hash, but encoding transfer-relevant update structure. Beyond source selection, the same signatures and marginals provide a diagnostic instrument for studying whether LLM task similarity is driven by activations, errors, or their coupling; shared-parameter and internal-layer validations, together with Llama-3.1-8B verbalizer-shift experiments, show that FisherSketch remains informative when activation similarity cannot distinguish tasks.

Poster
Bayes-inspired Integration of Pretrained Priors and Few-Shot Evidence for Few-Shot Classification

Mingyang Zhou, Xiaoxuan Zhang, Gang Liu, Yuhong Feng, Xiaoqun Wu, Hao Liao, Rui Mao

展开摘要

Few-shot classification aims to adapt a pretrained model to novel classes with limited examples. While current methods often heuristically combine pretrained knowledge and few-shot evidence, we seek a more principled understanding of their relationship. In this paper, we propose a Bayesian-inspired optimal integration framework(BOIF) that interprets pretrained models as priors and few-shot evidence as likelihoods. Under conditional independence approximation, we show that the optimal log-posterior decomposes into the sum of prior logits and likelihood logits. This leads to a simple yet effective design principle: decouple the prior and likelihood pathways and combine their logits additively. Guided by this principle, we implement BOIF using CLIP with two novel enhancements: (1) a multi-level feature adapter to enrich visual representations, and (2) a simplified cache module for likelihood estimation. Extensive experiments on 11 benchmarks show BOIF achieves state-of-the-art performance (e.g., 80.61\% average accuracy at 16-shot) and strong out-of-distribution robustness. Our work provides both a principled perspective and an effective instantiation for few-shot adaptation.

Poster
Auto-regressive In-context Demonstration Selection

Yunzhe Qi, Sirui Chen, Jiaru Zou, Jingrui He

展开摘要

Effective demonstration selection is crucial for maximizing large language model (LLM) performance in few-shot in-context learning. Because of effects such as recency bias, the effectiveness of demonstrations depends heavily on their contextual relationship to the specific query and on the ordering in which they are presented, making demonstration selection a complex combinatorial problem. To address these two challenges, we introduce AutoSelect, a novel framework that formulates demonstration selection as an auto-regressive sequential decision process. At each step, AutoSelect embeds the query and previously selected demonstrations into matrix representations to preserve structural information, and a trainable policy model sequentially selects the next best exemplar. To navigate the factorial space of demonstration permutations, our framework formulates a Kullback-Leibler (KL)-regularized optimization problem, from which an optimal policy induces an optimal Plackett-Luce (PL) ranking over all possible demonstration sequences. We prove that minimizing a tractable policy-level cross-entropy (CE) loss provably bounds the worst-case discrepancy between our policy's induced PL ranking and the optimal one, enabling tractable prioritization of high-quality sequences. Empirically, AutoSelect outperforms existing heuristic and learning-based methods across nine diverse datasets, achieving up to an 11\% improvement over the strongest baseline. Analytical studies and a case study further highlight AutoSelect's key properties, as well as its transferability and generalizability.

Poster
What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies

Fan Zhang, Shiming Fan, Hua Wang

展开摘要

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from “more interaction” to “more effective interaction”.

Poster
Forward-Chaining Temporal Point Process

Chao Yang, Wendi Ren, Shuang Li

展开摘要

Event sequences from complex systems, such as clinical workflows, are often sparse and incomplete. As a result, downstream models are trained on data that only partially captures the underlying dynamics. Synthetic sequence generation can augment real data by filling in missing structure and improving coverage of rare patterns, but generated trajectories must remain realistic, satisfy domain constraints, and allow control. We propose the Forward-Chaining Temporal Point Process (FC-TPP), a framework for constraint-aware and controllable sequence generation in continuous time. FC-TPP maintains an explicit latent symbolic state encoding high-level predicates, which evolves through a differentiable multi-hop forward-chaining operator. Logical rules update the latent state based on recent events, while a temporal point process decoder generates future event times and types conditioned on this evolving state. By tying the generative dynamics to multi-hop reasoning in latent space, FC-TPP incorporates symbolic structure throughout generation rather than relying directly on raw event histories. Experiments on synthetic data and four semi-synthetic/real-world benchmarks—LogiCity, MIMIC-IV, EPIC-100, and IKEA ASM—show that FC-TPP achieves higher generation quality under limited and incomplete data, with stronger constraint adherence and greater controllability than purely neural and prior neuro-symbolic baselines.

Poster
LearniBridge: Learnable Calibration of Feature Caching for Diffusion Models Acceleration

Xuyue Huang, Zhe Chen, Wang Shen, Xiao-Ping Zhang

展开摘要

Diffusion Transformers (DiTs) have driven substantial progress in image and video generation but suffer from prohibitive computational costs. Feature caching accelerates inference by reusing intermediate representations. Existing methods rely on historical features for implementation simplicity, yet suffer from severe error accumulation at high acceleration ratios. To address this limitation, we investigate the nature of the requisite feature correction. We demonstrate that the optimal calibration update is characterized by a shared low-rank subspace across diverse prompts. Guided by this structural insight, we propose LearniBridge, a learnable calibration mechanism for feature caching that bridges multiple timesteps through lightweight LoRA updates. This mechanism enables effective calibration requiring only $3-5$ training samples. Extensive experiments on image and video generation show that LearniBridge achieves up to $5.87\times$, $5.75\times$, and $4.10\times$ acceleration on FLUX, HunyuanVideo, and WAN 2.1, respectively. On WAN 2.1, it improves VBench by 1.28\% over the previous SOTA at $4.10\times$ acceleration.

Poster
TabPack: Efficient Hyperparameter Ensembles for Tabular Deep Learning

Yury Gorishniy, Akim Kotelnikov, Ivan Rubachev, Artem Babenko

展开摘要

Deep learning models for supervised learning on tabular data are rapidly improving. Notably, ensembles (mixtures of multiple models) often play an important role in achieving top performance, which motivates designing _ensemble-first_ systems rather than treating ensembling as an ad hoc trick. In this work, we present TabPack — a new ensembling approach that packs many base model–optimizer pairs with different hyperparameters into a single neural network and a single optimizer. The base model and optimizer hyperparameters are sampled randomly, after which all base models are trained in parallel, and the final ensemble is built on the fly during training. As a result, TabPack produces powerful ensembles in a single run, with substantial efficiency gains over traditional approaches. With its remarkable efficiency, strong performance on medium-to-large datasets, and reduced reliance on traditional hyperparameter tuning, TabPack is an appealing solution for practitioners and researchers that makes tabular DL more accessible on consumer-grade hardware and suggests a new avenue for designing better tabular deep learning systems.

Poster
Mem-T: Densifying Rewards for Long-Horizon Memory Agents

Yanwei Yue, Guibin Zhang, Boci Peng, Xuanbo Fan, Jiaxin Guo, Qiankun Li, Yan Zhang

展开摘要

Memory agents, which depart from predefined memory-processing pipelines by endogenously managing the processing, storage, and retrieval of memories, have garnered increasing attention for their autonomy and adaptability. However, existing training paradigms remain constrained: agents often traverse long-horizon sequences of memory operations before receiving sparse and delayed rewards, which hinders truly end-to-end optimization of memory management policies. To address this limitation, we introduce Mem-T, an autonomous memory agent that interfaces with a lightweight hierarchical memory database to perform dynamic updates and multi-turn retrieval over streaming inputs. To effectively train long-horizon memory management capabilities, we further propose MoT-GRPO, a tree-guided reinforcement learning framework that transforms sparse terminal feedback into dense, step-wise supervision via memory operation tree backpropagation and hindsight credit assignment, thereby enabling the joint optimization of memory construction and retrieval. Extensive experiments demonstrate that Mem-T is **(1) high-performing**, surpassing frameworks such as A-Mem and Mem0 by up to $14.94\\%$, and **(2) economical**, operating on a favorable accuracy-efficiency Pareto frontier and reducing inference tokens per query by $\sim24.45\\%$ relative to GAM without sacrificing performance.

Poster
Olmix: A Framework for Data Mixing Throughout LM Development

Mayee F Chen, Tyler Murray, David Heineman, Matt Jordan, Hannaneh Hajishirzi, Christopher Re, Luca Soldaini, Kyle Lo

展开摘要

Data mixing---determining the ratios of data from different domains---is a first-order concern for training language models (LMs), but existing mixing methods have poorly understood design choices and assume that the set of domains remain fixed throughout development. We present Olmix, a framework that addresses two challenges encountered during LM development. First, the configuration space for developing a mixing method is not well understood---design choices across existing methods lack justification or consensus and overlook practical issues like data constraints. We conduct a comprehensive empirical study of this space, identifying which design choices lead to a strong mixing method. Second, the domain set evolves throughout LM development as datasets are revised and expanded---a problem setting largely unaddressed by existing works. We study how to efficiently recompute the mixture after the domain set is updated, given an existing mix from before the update. We introduce mixture reuse, a mechanism that reuses existing relative ratios and recomputes ratios only for domains affected by an update. Over a sequence of five domain-set updates mirroring real-world LM development, mixture reuse matches the performance of fully recomputing the mix after each update with 74% less compute and improves over training without mixing by 11.6% on downstream tasks.

Poster
Strategy Executability in Mathematical Reasoning: Leveraging Human–Model Differences for Effective Guidance

Weida Liang, Yiyou Sun, Shuyuan Nan, Chuang Li, Dawn Song, Kenji Kawaguchi

展开摘要

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models—even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between *strategy usage*—whether a reasoning strategy appears in successful solutions—and *strategy executability*—whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose *Selective Strategy Retrieval* (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to $+13$ points on AIME25 and $+5$ points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.

Poster
TD-VAD: Breaking Visual Dependence in Video Anomaly Detection with Text-Driven Learning

Shuangqing Zhang, Lei-Lei Ma, Lei-Lei Ma, Zhao Wang, Wen Dong, Xinyi Xu, Guo-Sen Xie, Guo-Sen Xie, Caifeng Shan, Fang Zhao

展开摘要

Visual data is typically a prerequisite for training existing video anomaly detection (VAD) methods. However, obtaining sufficient annotated anomaly data for training is challenging and not scalable due to the rarity of anomaly data and the wide variety of abnormal events. In this work, we advocate that the effectiveness of treating texts as video sequences for the VAD model and propose a novel Text-Driven Video Anomaly Detection (TD-VAD) approach to break visual dependence. In contrast to the anomaly video data, text descriptions of abnormal events are easy to collect, and their class labels can be directly derived. Specifically, our method utilizes video-like text descriptions with temporal characteristics generated by LLM to train a VAD model, without any reliance on target-domain anomaly data. To capture the long and short-range temporal logic of events, we design the event evolution causal attention module to model contextual dependencies across time. During inference, considering the domain gap between the texts and video sequences, we use the frozen CLIP encoder to extract embeddings of video frames to align the text modality while retaining crucial visual information. Comprehensive experiments on two large-scale VAD datasets, XD-Violence and UCF-Crime, demonstrate that our method outperforms prior one-class and unsupervised VAD methods by a large margin.

Poster
EGG: An Expert-Guided Agent Framework for Kernel Generation

Yaochen Han, Ke Fan, Hongxu Jiang, Wanqi Xu, Weiyu Xie, Runhua Zhang, Chenhui Zhu, Yixiang Zhang

展开摘要

High-performance GPU kernels are critical for reducing the exponentially growing computational costs of large language models (LLMs), but their development heavily relies on manual tuning by domain experts. While recent advances in LLM-based approaches show promise for automating kernel generation, they still struggle to achieve both correctness and high performance. This limitation primarily arises from the lack of domain-specific optimization guidance, hindering effective exploration of the optimization space. We propose $\textbf{EGG}$, an $\underline{E}$xpert-$\underline{G}$uided Agent Framework for Kernel $\underline{G}$eneration, which incorporates expert optimization principles to guide LLMs’ decisions. Inspired by expert workflows, we decompose kernel generation into two hierarchical stages: 1) algorithmic structure design, which establishes a high-quality computational structure foundation; 2) hardware-specific tuning, which performs targeted adjustments through parallel mapping, tensor tiling, and memory optimization. This staged decomposition defines explicit optimization objectives, structuring the design space to achieve progressive refinements. To this end, a stage-aware multi-agent collaboration mechanism is designed for inter and intra-stage context management, ensuring stable optimization trajectories. Experiments on KernelBench and real-world workloads show that EGG achieves a $2.13\times$ average speedup over PyTorch, outperforming existing agent-based and RL-based approaches.

Poster
AOrchestra: Automating Sub-Agent Creation for Agentic Orchestration

Jianhao Ruan, Zhihao Xu, Yiran Peng, Fashen Ren, Zhaoyang Yu, Xinbing Liang, Jinyu Xiang, Yongru Chen, Bang Liu, Chenglin Wu, Yuyu Luo, Jiayi Zhang

展开摘要

Language agents have shown strong promise for task automation. Realizing this promise for increasingly complex, long-horizon tasks has driven the rise of a subagent-as-tools paradigm for multi-turn task solving. However, existing designs still lack a dynamic abstraction view of sub-agents, thereby hurting adaptability: sub-agents are either context-isolated threads that lack specialization, or static roles that require human-engineering. We address this challenge with a unified, framework-agnostic agent abstraction that models any agent as a tuple (Model, Task, Tools, Context). This tuple acts as a compositional recipe for capabilities, enabling the system to spawn specialized executors for each task on demand. Building on this abstraction, we introduce an agentic system AOrchestra, where the central orchestrator concretizes the tuple at each step: it curates task-relevant context, selects tools and models, and delegates execution via on-the-fly automatic agent creation. Such designs enable reducing human engineering efforts, and remain framework-agnostic with plug-and-play support for diverse agents as task executors. It also enables a controllable performance–cost trade-off, allowing the system to approach Pareto-efficient. Across three challenging benchmarks and environments (GAIA, SWE-Bench, Terminal-Bench), AOrchestra achieves 16.28% relative improvement against the strongest baseline when paired with Gemini-3-Flash.

Poster
Executable Agentic Memory for GUI Agent

Zerui Qin, Sheng Yue, Xingyuan Hua, Yongjian Fu, Ju Ren

展开摘要

Modern GUI agents typically rely on a model-centric and step-wise interaction paradigm, where LLMs must re-interpret the UI and re-decide actions at every screen, which is fragile in long-horizon tasks. In this paper, we propose Executable Agentic Memory (EAM), a structured Knowledge Graph (KG) that shifts GUI planning from free-form generation to a robust retrieval-and-execution process. Our approach includes a sample-efficient memory construction pipeline using state-aware DFS and action-group mining to compress multi-step routines. To ensure efficient planning, we introduce a value-guided graph search where a lightweight Q-function model steers Monte Carlo Tree Search (MCTS) over the KG. We theoretically establish bias-consistency for the Q-model and derive sample complexity bounds for path recovery. Empirically, EAM outperforms state-of-the-art baselines like UI-TARS-7B by up to $19.6\%$ on AndroidWorld, while reducing token costs $6\times$ relative to GPT-4o. With a $2.8$s average latency, EAM enables reliable, quick, and long-horizon GUI automation.

Poster
Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding

Rustem Takhanov, Zhenisbek Assylbekov

展开摘要

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method --- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR --- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by $\mathcal{F}$, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by $\mathcal{O}(1/\sqrt{N})$, where $N$ is the sample size and the hidden constant depends on the class $\mathcal{F}$ and the input distribution. This reduction enables us to analyze conditional KRR in the case where $K$ is positive definite and $\mathcal{F}$ is given by the first $k$ principal eigenfunctions in the Mercer decomposition of $K$. We also consider the setting where $\mathcal{F}$ consists of $k$ random features from a random feature representation of $K$. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the $\mathcal{F}$-component of the regression function is more pronounced than the residual part.

Poster