Back in my student years, I had a book by a rather famous Dane about a rather famous programming language. And although I harbored genuine warm feelings for C++, I couldn’t get through even half of that book—the reading was that dreary. Well, it didn’t stop me from continuing to believe in the destiny fate had in store for me and C++. So, in the summer of 2011, I went to interview for a C++ developer. This is […]
arXiv:2602.16537v2 Announce Type: replace-cross Abstract: We study online conformal prediction for non-stationary data streams subject to unknown distribution drift. While most prior work studied this problem under adversarial settings and/or assessed performance in terms of gaps of time-averaged marginal coverage, we instead evaluate performance through training-conditional cumulative regret. We specifically focus on independently generated data with two types of distribution shift: abrupt change points and smooth drift. When non-conformity score functions are pretrained on an independent dataset, we […]
arXiv:2601.23236v2 Announce Type: replace-cross Abstract: We propose a variational framework that interprets transformer layers as iterations of an optimization algorithm acting on token embeddings. In this view, self-attention implements a gradient step of an interaction energy, while MLP layers correspond to gradient updates of a potential energy. Standard GPT-style transformers emerge as vanilla gradient descent on the resulting composite objective, implemented via Lie–Trotter splitting between these two energy functionals. This perspective enables principled architectural design using classical optimization […]
arXiv:2512.17805v2 Announce Type: replace-cross Abstract: We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove information-theoretic lower bounds together with matching or near-matching upper bounds, covering both fixed and random designs under Hilbert-valued Gaussian noise and Gaussian white noise errors. The rates are controlled by the spectrum of the covariance operator of the measure […]
arXiv:2512.12988v2 Announce Type: replace-cross Abstract: Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the latent subpopulation distributions may be unrealistic, which motivates the need for nonparametric modeling of the mixture components themselves. In this paper, we study finite mixtures with nonparametric mixture components, using a Bayesian nonparametric modeling approach. In particular, it is […]
arXiv:2510.07093v3 Announce Type: replace-cross Abstract: Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of conformalized regression commonly treats the miscoverage level $alpha$ as a fixed constant. In this work, we establish non-asymptotic bounds on the deviation of the prediction set length from the oracle interval length for conformalized quantile and median regression trained via […]
arXiv:2506.14020v4 Announce Type: replace-cross Abstract: Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing a probability path that interpolates between reference and data distributions. However, these methods typically model the evolution of individual nodes and edges independently and use linear interpolations in the disjoint space of nodes/edges to build the path. This disentangled interpolation breaks […]
arXiv:2506.08921v2 Announce Type: replace-cross Abstract: We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far, has focused on models with a limited number of inputs due to the challenges of creating uniform partitions in high dimensions. To overcome these challenges, we propose a simple methodology for constructing an effective stratification of the input domain […]
arXiv:2505.13770v2 Announce Type: replace-cross Abstract: Reliable causal inference is essential for making decisions in high-stakes areas like medicine, economics, and public policy. However, it remains unclear whether large language models (LLMs) can handle rigorous and trustworthy statistical causal inference. Current benchmarks usually involve simplified tasks. For example, these tasks might only ask LLMs to identify semantic causal relationships or draw conclusions directly from raw data. As a result, models may overlook important statistical pitfalls, such as Simpson’s paradox […]
arXiv:2502.11682v2 Announce Type: replace-cross Abstract: Strong Differential Privacy (DP) and Optimization guarantees are two desirable properties for a method in Federated Learning (FL). However, existing algorithms do not achieve both properties at once: they either have optimal DP guarantees but rely on restrictive assumptions such as bounded gradients/bounded data heterogeneity, or they ensure strong optimization performance but lack DP guarantees. To address this gap in the literature, we propose and analyze a new method called Clip21-SGD2M based on […]
