In this work, we focus on a novel and practical task, i.e., Time-vAriant iMage inPainting (TAMP). The aim of TAMP is to restore a damaged target image by leveraging the complementary information from a reference image, where both images captured the same scene but with a significant time gap in between, i.e., time-variant images. Different from conventional reference-guided image inpainting, the reference image under TAMP setup presents significant content distinction to the target image and potentially also suffers from damages. Such an application frequently happens in our daily lives to restore a damaged image by referring to another reference image, where there is no guarantee of the reference image's source and quality. In particular, our study finds that even state-of-the-art (SOTA) reference-guided image inpainting methods fail to achieve plausible results due to the chaotic image complementation. To address such an ill-posed problem, we propose a novel Interactive Distribution Transition Estimation (InDiTE) module which interactively complements the time-variant images with adaptive semantics thus facilitate the restoration of damaged regions. To further boost the performance, we propose our TAMP solution, namely Interactive Distribution Transition Estimation-driven Diffusion (InDiTE-Diff), which integrates InDiTE with SOTA diffusion model and conducts latent cross-reference during sampling. Moreover, considering the lack of benchmarks for TAMP task, we newly assembled a dataset, i.e., TAMP-Street, based on existing image and mask datasets. We conduct experiments on the TAMP-Street datasets under two different time-variant image inpainting settings, which show our method consistently outperform SOTA reference-guided image inpainting methods for solving TAMP.

Amyotrophic lateral sclerosis (ALS) is a degenerative disorder of motor neurons that causes progressive paralysis in patients. Current treatment options aim to prolong survival and improve quality of life; however, due to the heterogeneity of the disease, it is often difficult to determine the optimal time for potential therapies or medical interventions. In this study, we propose a novel method to predict the time until a patient with ALS experiences significant functional impairment (ALSFRS-R<=2) with respect to five common functions: speaking, swallowing, handwriting, walking and breathing. We formulate this task as a multi-event survival problem and validate our approach in the PRO-ACT dataset by training five covariate-based survival models to estimate the probability of an event over a 500-day period after a baseline visit. We then predict five event-specific individual survival distributions (ISDs) for each patient, each providing an interpretable and meaningful estimate of when that event will likely take place in the future. The results show that covariate-based models are superior to the Kaplan-Meier estimator at predicting time-to-event outcomes. Additionally, our method enables practitioners to make individual counterfactual predictions, where certain features (covariates) can be changed to see their effect on the predicted outcome. In this regard, we find that Riluzole has little to no impact on predicted functional decline. However, for patients with bulbar-onset ALS, our method predicts considerably shorter counterfactual time-to-event estimates for tasks related to speech and swallowing compared to limb-onset ALS. The proposed method can be applied to current clinical examination data to assess the risk of functional decline and thus allow more personalized treatment planning.

Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as hypotheses -- and the goal is to determine which one best describes the underlying data distribution. This problem is known to be solvable very efficiently, requiring roughly $O(\log n)$ samples and running in $\tilde{O}(n)$ time. The quality of the output is measured via the total variation distance to the unknown distribution, and the approximation factor of the algorithm determines how large this distance is compared to the optimal distance achieved by the best candidate hypothesis. It is known that $α= 3$ is the optimal approximation factor for this problem. We study hypothesis selection under the constraint of differential privacy. We propose a differentially private algorithm in the central model that runs in nearly-linear time with respect to the number of hypotheses, achieves the optimal approximation factor, and incurs only a modest increase in sample complexity, which remains polylogarithmic in $n$. This resolves an open question posed by [Bun, Kamath, Steinke, Wu, NeurIPS 2019]. Prior to our work, existing upper bounds required quadratic time.

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.

The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.

This paper studies the approximation and generalization abilities of score-based neural network generative models (SGMs) in estimating an unknown distribution $P_0$ from $n$ i.i.d. observations in $d$ dimensions. Assuming merely that $P_0$ is $α$-sub-Gaussian, we prove that for any time step $t \in [t_0, n^{O(1)}]$, where $t_0 \geq O(α^2n^{-2/d}\log n)$, there exists a deep ReLU neural network with width $\leq O(\log^3n)$ and depth $\leq O(n^{3/d}\log_2n)$ that can approximate the scores with $\tilde{O}(n^{-1})$ mean square error and achieve a nearly optimal rate of $\tilde{O}(n^{-1}t_0^{-d/2})$ for score estimation, as measured by the score matching loss. Our framework is universal and can be used to establish convergence rates for SGMs under milder assumptions than previous work. For example, assuming further that the target density function $p_0$ lies in Sobolev or Besov classes, with an appropriately early stopping strategy, we demonstrate that neural network-based SGMs can attain nearly minimax convergence rates up to logarithmic factors. Our analysis removes several crucial assumptions, such as Lipschitz continuity of the score function or a strictly positive lower bound on the target density.

Reinforcement learning (RL) typically models the interaction between the agent and environment as a Markov decision process (MDP), where the rewards that guide the agent's behavior are always observable. However, in many real-world scenarios, rewards are not always observable, which can be modeled as a monitored Markov decision process (Mon-MDP). Prior work on Mon-MDPs have been limited to simple, tabular cases, restricting their applicability to real-world problems. This work explores Mon-MDPs using function approximation (FA) and investigates the challenges involved. We show that combining function approximation with a learned reward model enables agents to generalize from monitored states with observable rewards, to unmonitored environment states with unobservable rewards. Therefore, we demonstrate that such generalization with a reward model achieves near-optimal policies in environments formally defined as unsolvable. However, we identify a critical limitation of such function approximation, where agents incorrectly extrapolate rewards due to overgeneralization, resulting in undesirable behaviors. To mitigate overgeneralization, we propose a cautious police optimization method leveraging reward uncertainty. This work serves as a step towards bridging this gap between Mon-MDP theory and real-world applications.

The optimization of bidding strategies for online advertising slot auctions presents a critical challenge across numerous digital marketplaces. A significant obstacle to the development, evaluation, and refinement of real-time autobidding algorithms is the scarcity of comprehensive datasets and standardized benchmarks. To address this deficiency, we present an auction benchmark encompassing the two most prevalent auction formats. We implement a series of robust baselines on a novel dataset, addressing the most salient Real-Time Bidding (RTB) problem domains: budget pacing uniformity and Cost Per Click (CPC) constraint optimization. This benchmark provides a user-friendly and intuitive framework for researchers and practitioners to develop and refine innovative autobidding algorithms, thereby facilitating advancements in the field of programmatic advertising. The implementation and additional resources can be accessed at the following repository (https://github.com/avito-tech/bat-autobidding-benchmark, https://doi.org/10.5281/zenodo.14794182).

--Label distribution learning (LDL) is an emerging learning paradigm designed to capture the relative importance of labels for each instance. Label-specific features (LSFs), constructed by LIFT, have proven effective for learning tasks with label ambiguity by leveraging clustering-based prototypes for each label to re-characterize instances. However, directly introducing LIFT into LDL tasks can be suboptimal, as the prototypes it collects primarily reflect intra-cluster relationships while neglecting interactions among distinct clusters. Additionally, constructing LSFs using multi-perspective information, rather than relying solely on Euclidean distance, provides a more robust and comprehensive representation of instances, mitigating noise and bias that may arise from a single distance perspective. T o address these limitations, we introduce Structural Anchor Points (SAPs) to capture inter-cluster interactions. This leads to a novel LSFs construction strategy, LIFT -SAP, which enhances LIFT by integrating both distance and direction information of each instance relative to SAPs. Furthermore, we propose a novel LDL algorithm, Label Distribution Learning via Label-specifIc FeaT ure with SAPs (LDL-LIFT -SAP), which unifies multiple label description degrees predicted from different LSF spaces into a cohesive label distribution. Extensive experiments on 15 real-world datasets demonstrate the effectiveness of LIFT -SAP over LIFT, as well as the superiority of LDL-LIFT -SAP compared to seven other well-established algorithms. Index T erms --Label distribution learning, Label-specific features, Structural anchor points, Prototypes, Direction information.

Cluster weighted models with multivariate skewed distributions for functional data Cristina Anton, 1 Roy Shivam Ram Shreshtth 2 1 Department of Mathematics and Statistics, MacEwan University, 103C, 10700-104 Ave., Edmonton, AB T5J 4S2, Canada, email: popescuc@macewan.ca 2 Department of Mathematics and Statistics, Indian Institute of Technology Kanpur Abstract We propose a clustering method, funWeightClustSkew, based on mixtures of functional linear regression models and three skewed multivariate distributions: the variance-gamma distribution, the skew-t distribution, and the normal-inverse Gaussian distribution. Our approach follows the framework of the functional high dimensional data clustering (funHDDC) method, and we extend to functional data the cluster weighted models based on skewed distributions used for finite dimensional multivariate data. We consider several parsimonious models, and to estimate the parameters we construct an expectation maximization (EM) algorithm. We illustrate the performance of funWeightClustSkew for simulated data and for the Air Quality dataset. Keywords: Cluster weighted models, Functional linear regression, EM algorithm, Skewed distributions, Multivariate functional principal component analysis 1 Introduction Smart devices and other modern technologies record huge amounts of data measured continuously in time. These data are better represented as curves instead of finite-dimensional vectors, and they are analyzed using statistical methods specific to functional data (Ramsay and Silverman, 2006; Ferraty and Vieu, 2006; Horv ath and Kokoszka, 2012). Many times more than one curve is collected for one individual, e.g.