Learning with identical train and test distributions has been extensively investigated both practically and theoretically. Much remains to be understood, however, in statistical learning under distribution shifts. This paper focuses on a distribution shift setting where train and test distributions can be related by classes of (data) transformation maps. We initiate a theoretical study for this framework, investigating learning scenarios where the target class of transformations is either known or unknown. We establish learning rules and algorithmic reductions to Empirical Risk Minimization (ERM), accompanied with learning guarantees. We obtain upper bounds on the sample complexity in terms of the VC dimension of the class composing predictors with transformations, which we show in many cases is not much larger than the VC dimension of the class of predictors. We highlight that the learning rules we derive offer a game-theoretic viewpoint on distribution shift: a learner searching for predictors and an adversary searching for transformation maps to respectively minimize and maximize the worst-case loss.

Accurate and robust 3D object detection is a critical component in autonomous vehicles and robotics. While recent radar-camera fusion methods have made significant progress by fusing information in the bird's-eye view (BEV) representation, they often struggle to effectively capture the motion of dynamic objects, leading to limited performance in real-world scenarios. In this paper, we introduce CRT-Fusion, a novel framework that integrates temporal information into radar-camera fusion to address this challenge. Our approach comprises three key modules: Multi-View Fusion (MVF), Motion Feature Estimator (MFE), and Motion Guided Temporal Fusion (MGTF).

Deep learning based neural decoding from stereotactic electroencephalography (sEEG) would likely benefit from scaling up both dataset and model size. To achieve this, combining data across multiple subjects is crucial. However, in sEEG cohorts, each subject has a variable number of electrodes placed at distinct locations in their brain, solely based on clinical needs. Such heterogeneity in electrode number/placement poses a significant challenge for data integration, since there is no clear correspondence of the neural activity recorded at distinct sites between individuals. Here we introduce seegnificant: a training framework and architecture that can be used to decode behavior across subjects using sEEG data.

This paper explores the realm of infinite horizon average reward Constrained Markov Decision Processes (CMDPs). To the best of our knowledge, this work is the first to delve into the regret and constraint violation analysis of average reward CMDPs with a general policy parametrization. To address this challenge, we propose a primal dual-based policy gradient algorithm that adeptly manages the constraints while ensuring a low regret guarantee toward achieving a global optimal policy.

Given a source and a target probability measure, the Monge problem studies efficient ways to map the former onto the latter.This efficiency is quantified by defining a *cost* function between source and target data.

Deep neural networks (DNNs) have recently achieved remarkable advancements in time series forecasting (TSF) due to their powerful ability of sequence dependence modeling. To date, existing DNN-based TSF methods still suffer from unreliable predictions for real-world data due to its non-stationarity characteristics, i.e., data distribution varies quickly over time. To mitigate this issue, several normalization methods (e.g., SAN) have recently been specifically designed by normalization in a fixed period/window in the time domain. However, these methods still struggle to capture distribution variations, due to the complex time patterns of time series in the time domain. Based on the fact that wavelet transform can decompose time series into a linear combination of different frequencies, which exhibits distribution variations with time-varying periods, we propose a novel Dual-domain Dynamic Normalization (DDN) to dynamically capture distribution variations in both time and frequency domains. Specifically, our DDN tries to eliminate the non-stationarity of time series via both frequency and time domain normalization in a sliding window way. Besides, our DDN can serve as a plug-in-play module, and thus can be easily incorporated into other forecasting models. Extensive experiments on public benchmark datasets under different forecasting models demonstrate the superiority of our DDN over other normalization methods. Code will be made available following the review process.

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb{R}^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal{O}\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nyström-based one) on $\mathbb{R}^d$.

Tabular data is a pervasive modality spanning a wide range of domains, and this inherent diversity poses a considerable challenge for deep learning. Recent advancements using transformer-based in-context learning have shown promise on smaller and less complex tabular datasets, but have struggled to scale to larger and more complex ones. To address this limitation, we propose a combination of retrieval and fine-tuning: we can adapt the transformer to a local subset of the data by collecting nearest neighbours, and then perform task-specific fine-tuning with this retrieved set of neighbours in context. Using TabPFN as the base model -- currently the best tabular in-context learner -- and applying our retrieval and fine-tuning scheme on top results in what we call a locally-calibrated PFN, or LoCalPFN. We conduct extensive evaluation on 95 datasets curated by TabZilla from OpenML, upon which we establish a new state-of-the-art with LoCalPFN -- even with respect to tuned tree-based models. Notably, we show a significant boost in performance compared to the base in-context model, demonstrating the efficacy of our approach and advancing the frontier of deep learning in tabular data.

Humans naturally retain memories of permanent elements, while ephemeral moments often slip through the cracks of memory. This selective retention is crucial for robotic perception, localization, and mapping. To endow robots with this capability, we introduce 3D Gaussian Mapping (3DGM), a self-supervised, camera-only offline mapping framework grounded in 3D Gaussian Splatting.

How Bad Is Plagiarism, Really? From ancient Rome to the era of A.I., people have prized originality, but the line where influence ends and cribbing begins is notoriously blurry. One pleasing facet of plagiarism is that, in the eyes of the law, it doesn't exist. I could come over later, bring a few beers, and we could, you know, get down to some serious humanizing. Hard to resist, these days, given what's at stake. For students with assignments to complete, who have already vanquished their desolation by asking ChatGPT to compose an essay on their behalf, a humanizer is an A.I. tool that takes what has been produced, puts it through a further digital mill, and makes it sound as if it had emerged from a verifiable person. Among the companies that offer such tools are StealthWriter, HIX AI, and QuillBot. Anyone who has buttered and blitzed a mountain of mashed potatoes into a purée will understand.