Related papers: Reverse Information Projections and Optimal E-stat…
We consider testing a composite null hypothesis $\mathcal{P}$ against a point alternative $\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\mathbb{E}_\mathsf{P}[X] \leq 1$ for every $\mathsf{P} \in…
Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
We derive the unique e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, hereby contributing with the first application beyond the assumption of mutually absolutely continuous…
This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint…
The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…
Inverse Reinforcement Learning (IRL) learns a reward function to explain expert demonstrations. Modern IRL methods often use the adversarial (minimax) formulation that alternates between reward and policy optimization, which often lead to…
We analyze common types of e-variables and e-processes for composite exponential family nulls: the optimal e-variable based on the reverse information projection (RIPr), the conditional (COND) e-variable, and the universal inference (UI)…
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the…
Reinforcement Learning with Verifiable Rewards (RLVR) has become a central post-training paradigm for improving the reasoning capabilities of large language models. Yet existing methods share a common blind spot: they optimize policies…
For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…
Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the…
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…
Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…
Integrative analysis of multiple datasets for estimating optimal individualized treatment rules (ITRs) can enhance decision efficiency. A central challenge is posterior shift, wherein the conditional distribution of potential outcomes given…
The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…
In reinforcement learning, Reverse Experience Replay (RER) is a recently proposed algorithm that attains better sample complexity than the classic experience replay method. RER requires the learning algorithm to update the parameters…
In real-world applications of reinforcement learning (RL), noise from inherent stochasticity of environments is inevitable. However, current policy evaluation algorithms, which plays a key role in many RL algorithms, are either prone to…
On-policy reinforcement learning methods, like Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), often demand extensive data per update, leading to sample inefficiency. This paper introduces Reflective Policy…
We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…