arXiv subjects

Cambridge Yang

Publications and source records attributed to Cambridge Yang.

7 recordsLinked to original sources

arXiv2026

Archimedean Copula Inference via Taylor-Mode AD

No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and (c) exact parameter gradients. Existing implementations handle only bivariate problems, low dimensional (i.e., $d \leq 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present \textsc{acopula}, a JAX-native framework that, given any Archimedean generator -- classical or neural -- evaluates exact nested-copula likelihoods and parameter gradients under arbitrary censoring masks in polynomial time. The mechanism is polynomial powering of Taylor-mode automatic differentiation output, which replaces per-family hand-derived partial Bell polynomial tables with a single differentiable computation that any user-defined generator can drive. We conduct extensive simulations to verify the correctness of \textsc{acopula}. We then demonstrate (a) per-variable censoring on $85{,}229$ MIMIC-IV ICU admissions in high dimensions with $d{=}53$, fit by both classical Archimedean families and nested neural Archimedean copulas; (b) an 11-sector hierarchical model on S\&P~500 daily returns at $d{=}98$; (c) family-agnostic censored MLE across ten families, five of them with no prior implementation, on a retinopathy study; and (d) a ${\sim}650\times$ per-density speedup over R's \texttt{nacLL} at $d{=}35$, scaling quadratically to $d{=}8{,}000$.

cs.LG↗

arXiv2025

Benchmarking World-Model Learning with Environment-Level Queries

World models are central to building AI agents capable of flexible reasoning and planning. Yet current evaluations (i) test only properties measurable from observed interactions, such as next-frame prediction or task return, and (ii) do not test whether a learned model supports diverse queries about the environment. In contrast, humans build $\textit{general-purpose}$ models that can answer many different questions about an environment$\unicode{x2014}$including questions that require understanding global structure and counterfactual consequences. We propose $\textit{WorldTest}$: a protocol for evaluating whether agents learn models that support multiple $\textit{environment-level queries}\unicode{x2014}$questions whose answers depend on properties of the full environment, not just observed trajectories. Individually, these queries can target properties (e.g., reachability or the effects of interventions) that no single rollout distribution determines. Collectively, they assess model generality across query types. We instantiate WorldTest as $\textit{AutumnBench}$, a benchmark of 43 interactive grid-world environments and 129 tasks across three query families for both humans and learning agents. Experiments with 517 human participants and five frontier models show that humans substantially outperform these models, a gap we attribute to differences in exploration and belief updating. AutumnBench provides a framework for evaluating world-model learning in grid-world environments with environment-level queries, and WorldTest provides a template for extending such evaluations to richer domains.

cs.AI↗

arXiv2025

ExoPredicator: Learning Abstract Models of Dynamic Worlds for Robot Planning

Long-horizon embodied planning is challenging because the world does not only change through an agent's actions: exogenous processes (e.g., water heating, dominoes cascading) unfold concurrently with the agent's actions. We propose a framework for abstract world models that jointly learns (i) symbolic state representations and (ii) causal processes for both endogenous actions and exogenous mechanisms. Each causal process models the time course of a stochastic cause-effect relation. We learn these world models from limited data via variational Bayesian inference combined with LLM proposals. Across five simulated tabletop robotics environments, the learned models enable fast planning that generalizes to held-out tasks with more objects and more complex goals, outperforming a range of baselines.

cs.AI↗

arXiv2023

Computably Continuous Reinforcement-Learning Objectives are PAC-learnable

In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples and computation. In recent years, researchers have introduced objectives and corresponding reinforcement-learning algorithms beyond the classic cumulative rewards, such as objectives specified as linear temporal logic formulas. However, questions about the PAC-learnability of these new objectives have remained open. This work demonstrates the PAC-learnability of general reinforcement-learning objectives through sufficient conditions for PAC-learnability in two analysis settings. In particular, for the analysis that considers only sample complexity, we prove that if an objective given as an oracle is uniformly continuous, then it is PAC-learnable. Further, for the analysis that considers computational complexity, we prove that if an objective is computable, then it is PAC-learnable. In other words, if a procedure computes successive approximations of the objective's value, then the objective is PAC-learnable. We give three applications of our condition on objectives from the literature with previously unknown PAC-learnability and prove that these objectives are PAC-learnable. Overall, our result helps verify existing objectives' PAC-learnability. Also, as some studied objectives that are not uniformly continuous have been shown to be not PAC-learnable, our results could guide the design of new PAC-learnable objectives.

cs.LG↗

arXiv2022

On the (In)Tractability of Reinforcement Learning for LTL Objectives

In recent years, researchers have made significant progress in devising reinforcement-learning algorithms for optimizing linear temporal logic (LTL) objectives and LTL-like objectives. Despite these advancements, there are fundamental limitations to how well this problem can be solved. Previous studies have alluded to this fact but have not examined it in depth. In this paper, we address the tractability of reinforcement learning for general LTL objectives from a theoretical perspective. We formalize the problem under the probably approximately correct learning in Markov decision processes (PAC-MDP) framework, a standard framework for measuring sample complexity in reinforcement learning. In this formalization, we prove that the optimal policy for any LTL formula is PAC-MDP-learnable if and only if the formula is in the most limited class in the LTL hierarchy, consisting of formulas that are decidable within a finite horizon. Practically, our result implies that it is impossible for a reinforcement-learning algorithm to obtain a PAC-MDP guarantee on the performance of its learned policy after finitely many interactions with an unconstrained environment for LTL objectives that are not decidable within a finite horizon.

cs.AI↗

arXiv2021

Simplifying Dependent Reductions in the Polyhedral Model

A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics. Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sums, in which each component of the reduction's output potentially shares computation with another component in the reduction. Therefore an optimizing compiler can identify the computation shared between multiple components and generate code that computes the shared computation only once. These techniques, however, do not support reductions that -- when phrased in the language of the polyhedral model -- span multiple dependent statements. In such cases, existing approaches can generate incorrect code that violates the data dependences of the original, unoptimized program. In this work, we identify and formalize the optimization of dependent reductions as an integer bilinear program. We present a heuristic optimization algorithm that uses an affine sequential schedule of the program to determine how to simplfy reductions yet still preserve the program's dependences. We demonstrate that the algorithm provides optimal complexity for a set of benchmark programs from the literature on probabilistic inference algorithms, whose performance critically relies on simplifying these reductions. The complexities for 10 of the 11 programs improve siginifcantly by factors at least of the sizes of the input data, which are in the range of $10^4$ to $10^6$ for typical real application inputs. We also confirm the significance of the improvement by showing speedups in wall-clock time that range from $1.1\text{x}$ to over $10^6\text{x}$.

cs.PL↗

arXiv2018

Verifying Handcoded Probabilistic Inference Procedures

Researchers have recently proposed several systems that ease the process of performing Bayesian probabilistic inference. These include systems for automatic inference algorithm synthesis as well as stronger abstractions for manual algorithm development. However, existing systems whose performance relies on the developer manually constructing a part of the inference algorithm have limited support for reasoning about the correctness of the resulting algorithm. In this paper, we present Shuffle, a programming language for manually developing inference procedures that 1) enforces the basic rules of probability theory, 2) enforces the statistical dependencies of the algorithm's corresponding probabilistic model, and 3) generates an optimized implementation. We have used Shuffle to develop inference algorithms for several standard probabilistic models. Our results demonstrate that Shuffle enables a developer to deliver correct and performant implementations of these algorithms.

cs.PL↗