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We consider the classical online bipartite matching problem in the probe-commit model. In this problem, when an online vertex arrives, its edges must be probed to determine if they exist, based on known edge probabilities. A probing algorithm must respect commitment, meaning that if a probed edge exists, it must be used in the matching. Additionally, each online vertex has a patience constraint which limits the number of probes that can be made to an online vertex's adjacent edges. We introduce a new configuration linear program (LP) which we prove is a relaxation of an optimal offline probing algorithm. Using this LP, we establish the following competitive ratios which depend on the model used to generate the instance graph, and the arrival order of its online vertices: - In the worst-case instance model, an optimal $1/e$ ratio when the vertices arrive in uniformly at random (u.a.r.) order. - In the known independently distributed (i.d.) instance model, an optimal $1/2$ ratio when the vertices arrive in adversarial order, and a $1-1/e$ ratio when the vertices arrive in u.a.r. order. The latter two results improve upon the previous best competitive ratio of $0.46$ due to Brubach et al. (Algorithmica 2020), which only held in the more restricted known i.i.d. (independent and identically distributed) instance model. Our $1-1/e$-competitive algorithm matches the best known result for the prophet secretary matching problem due to Ehsani et al. (SODA 2018). Our algorithm is efficient and implies a $1-1/e$ approximation ratio for the special case when the graph is known. This is the offline stochastic matching problem, and we improve upon the $0.42$ approximation ratio for one-sided patience due to Pollner et al. (EC 2022), while also generalizing the $1-1/e$ approximation ratio for unbounded patience due to Gamlath et al. (SODA 2019).

At the beginning of 2022, a simplistic word-guessing game took the world by storm and was further adapted to many languages beyond the original English version. In this paper, we examine the strategies of daily word-guessing game players that have evolved during a period of over two years. A survey gathered from 25% of frequent players reveals their strategies and motivations for continuing the daily journey. We also explore the capability of several popular open-access large language model systems and open-source models at comprehending and playing the game in two different languages. Results highlight the struggles of certain models to maintain correct guess length and generate repetitions, as well as hallucinations of non-existent words and inflections.

We present a conformal inference method for constructing lower prediction bounds for survival times from right-censored data, extending recent approaches designed for type-I censoring. This method imputes unobserved censoring times using a suitable model, and then analyzes the imputed data using weighted conformal inference. This approach is theoretically supported by an asymptotic double robustness property. Empirical studies on simulated and real data sets demonstrate that our method is more robust than existing approaches in challenging settings where the survival model may be inaccurate, while achieving comparable performance in easier scenarios.

This paper presents a novel method to generate differentially private tabular datasets for hierarchical data, with a specific focus on origin-destination (O/D) trips. The approach builds upon the TopDown algorithm, a constraint-based mechanism designed to incorporate invariant queries into tabular data, developed by the US Census. O/D hierarchical data refers to datasets representing trips between geographical areas organized in a hierarchical structure (e.g., region $\rightarrow$ province $\rightarrow$ city). The developed method is crafted to improve accuracy on queries spanning wider geographical areas that can be obtained by aggregation. Maintaining high accuracy for aggregated geographical queries is a crucial attribute of the differentially private dataset, particularly for practitioners. Furthermore, the approach is designed to minimize false positives detection and to replicate the sparsity of the sensitive data. The key technical contributions of this paper include a novel TopDown algorithm that employs constrained optimization with Chebyshev distance minimization, with theoretical guarantees based on the maximum absolute error. Additionally, we propose a new integer optimization algorithm that significantly reduces the incidence of false positives. The effectiveness of the proposed approach is validated using both real-world and synthetic O/D datasets, demonstrating its ability to generate private data with high utility and a reduced number of false positives. We emphasize that the proposed algorithm is applicable to any tabular data with a hierarchical structure.

We introduce a novel, data-driven approach for reconstructing temporally coherent 3D motion from unstructured and potentially partial observations of non-rigidly deforming shapes. Our goal is to achieve high-fidelity motion reconstructions for shapes that undergo near-isometric deformations, such as humans wearing loose clothing. The key novelty of our work lies in its ability to combine implicit shape representations with explicit mesh-based deformation models, enabling detailed and temporally coherent motion reconstructions without relying on parametric shape models or decoupling shape and motion. Each frame is represented as a neural field decoded from a feature space where observations over time are fused, hence preserving geometric details present in the input data. Temporal coherence is enforced with a near-isometric deformation constraint between adjacent frames that applies to the underlying surface in the neural field. Our method outperforms state-of-the-art approaches, as demonstrated by its application to human and animal motion sequences reconstructed from monocular depth videos.

We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and size-distorted when some of the factors are weak. We propose estimators with improved rates of convergence and bias-aware CIs that remain valid uniformly, regardless of factor strength. Our approach applies the theory of minimax linear estimation to form a debiased estimate, using a nuclear norm bound on the error of an initial estimate of the interactive fixed effects. Our resulting bias-aware CIs take into account the remaining bias caused by weak factors. Monte Carlo experiments show substantial improvements over conventional methods when factors are weak, with minimal costs to estimation accuracy when factors are strong.

By generating new yet effective data, data augmentation has become a promising method to mitigate the data sparsity problem in sequential recommendation. Existing works focus on augmenting the original data but rarely explore the issue of imbalanced relevance and diversity for augmented data, leading to semantic drift problems or limited performance improvements. In this paper, we propose a novel Balanced data Augmentation Plugin for Sequential Recommendation (BASRec) to generate data that balance relevance and diversity. BASRec consists of two modules: Single-sequence Augmentation and Cross-sequence Augmentation. The former leverages the randomness of the heuristic operators to generate diverse sequences for a single user, after which the diverse and the original sequences are fused at the representation level to obtain relevance. Further, we devise a reweighting strategy to enable the model to learn the preferences based on the two properties adaptively. The Cross-sequence Augmentation performs nonlinear mixing between different sequence representations from two directions. It produces virtual sequence representations that are diverse enough but retain the vital semantics of the original sequences. These two modules enhance the model to discover fine-grained preferences knowledge from single-user and cross-user perspectives. Extensive experiments verify the effectiveness of BASRec. The average improvement is up to 72.0% on GRU4Rec, 33.8% on SASRec, and 68.5% on FMLP-Rec. We demonstrate that BASRec generates data with a better balance between relevance and diversity than existing methods. The source code is available at //github.com/KingGugu/BASRec.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.