We give new differentially private algorithms for the classic problems of learning decision lists and large-margin halfspaces in the PAC and online models. In the PAC model, we give a computationally efficient algorithm for learning decision lists with minimal sample overhead over the best non-private algorithms. In the online model, we give a private analog of the influential Winnow algorithm for learning halfspaces with mistake bound polylogarithmic in the dimension and inverse polynomial in the margin. As an application, we describe how to privately learn decision lists in the online model, qualitatively matching state-of-the art non-private guarantees.

Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be sufficient. Typically, thousands of shoes of the same size, make, and model are manufactured, any of which could be responsible for the print. Accordingly, a popular approach used by investigators is to examine the print for signs of ``accidentals,'' i.e., cuts, scrapes, and other features that accumulate on shoe soles after purchase due to wear. While some patterns of accidentals are common on certain types of shoes, others are highly distinctive, potentially distinguishing the suspect's shoe from all others. Quantifying the rarity of a pattern is thus essential to accurately measuring the strength of forensic evidence. In this study, we address this task by developing a hierarchical Bayesian model. Our improvement over existing methods primarily stems from two advancements. First, we frame our approach in terms of a latent Gaussian model, thus enabling inference to be efficiently scaled to large collections of annotated shoe prints via integrated nested Laplace approximations. Second, we incorporate spatially varying coefficients to model the relationship between shoes' tread patterns and accidental locations. We demonstrate these improvements through superior performance on held-out data, which enhances accuracy and reliability in forensic shoe print analysis.

Standard attention stores keys/values losslessly but reads them via a per-head convex average, blocking channel-wise selection. We propose the Free Energy Mixer (FEM): a free-energy (log-sum-exp) read that applies a value-driven, per-channel log-linear tilt to a fast prior (e.g., from queries/keys in standard attention) over indices. Unlike methods that attempt to improve and enrich the $(q,k)$ scoring distribution, FEM treats it as a prior and yields a value-aware posterior read at unchanged complexity, smoothly moving from averaging to per-channel selection as the learnable inverse temperature increases, while still preserving parallelism and the original asymptotic complexity ($O(T^2)$ for softmax; $O(T)$ for linearizable variants). We instantiate a two-level gated FEM that is plug-and-play with standard and linear attention, linear RNNs and SSMs. It consistently outperforms strong baselines on NLP, vision, and time-series at matched parameter budgets.

We study online learning in two-player uninformed Markov games, where the opponent's actions and policies are unobserved. In this setting, Tian et al. (2021) show that achieving no-external-regret is impossible without incurring an exponential dependence on the episode length $H$. They then turn to the weaker notion of Nash-value regret and propose a V-learning algorithm with regret $O(K^{2/3})$ after $K$ episodes. However, their algorithm and guarantee do not adapt to the difficulty of the problem: even in the case where the opponent follows a fixed policy and thus $O(\sqrt{K})$ external regret is well-known to be achievable, their result is still the worse rate $O(K^{2/3})$ on a weaker metric. In this work, we fully address both limitations. First, we introduce empirical Nash-value regret, a new regret notion that is strictly stronger than Nash-value regret and naturally reduces to external regret when the opponent follows a fixed policy. Moreover, under this new metric, we propose a parameter-free algorithm that achieves an $O(\min \{\sqrt{K} + (CK)^{1/3},\sqrt{LK}\})$ regret bound, where $C$ quantifies the variance of the opponent's policies and $L$ denotes the number of policy switches (both at most $O(K)$). Therefore, our results not only recover the two extremes -- $O(\sqrt{K})$ external regret when the opponent is fixed and $O(K^{2/3})$ Nash-value regret in the worst case -- but also smoothly interpolate between these extremes by automatically adapting to the opponent's non-stationarity. We achieve so by first providing a new analysis of the epoch-based V-learning algorithm by Mao et al. (2022), establishing an $O(ηC + \sqrt{K/η})$ regret bound, where $η$ is the epoch incremental factor. Next, we show how to adaptively restart this algorithm with an appropriate $η$ in response to the potential non-stationarity of the opponent, eventually achieving our final results.

Multivariate time series (MTS) anomaly diagnosis, which encompasses both anomaly detection and localization, is critical for the safety and reliability of complex, large-scale real-world systems. The vast majority of existing anomaly diagnosis methods offer limited theoretical insights, especially for anomaly localization, which is a vital but largely unexplored area. The aim of this contribution is to study the learning process of a Transformer when applied to MTS by revealing connections to statistical time series methods. Based on these theoretical insights, we propose the Attention Low-Rank Transformer (ALoRa-T) model, which applies low-rank regularization to self-attention, and we introduce the Attention Low-Rank score, effectively capturing the temporal characteristics of anomalies. Finally, to enable anomaly localization, we propose the ALoRa-Loc method, a novel approach that associates anomalies to specific variables by quantifying interrelationships among time series. Extensive experiments and real data analysis, show that the proposed methodology significantly outperforms state-of-the-art methods in both detection and localization tasks.

Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems, its performance hinges on the quality of the underlying reward model. Standard linear models suffer from high bias, while neural network approaches are often brittle and difficult to tune in online settings. Conversely, tree ensembles dominate tabular data prediction but typically rely on heuristic uncertainty quantification, lacking a principled probabilistic basis for TS. We propose Bayesian Forest Thompson Sampling (BFTS), the first contextual bandit algorithm to integrate Bayesian Additive Regression Trees (BART), a fully probabilistic sum-of-trees model, directly into the exploration loop. We prove that BFTS is theoretically sound, deriving an information-theoretic Bayesian regret bound of $\tilde{O}(\sqrt{T})$. As a complementary result, we establish frequentist minimax optimality for a "feel-good" variant, confirming the structural suitability of BART priors for non-parametric bandits. Empirically, BFTS achieves state-of-the-art regret on tabular benchmarks with near-nominal uncertainty calibration. Furthermore, in an offline policy evaluation on the Drink Less micro-randomized trial, BFTS improves engagement rates by over 30% compared to the deployed policy, demonstrating its practical effectiveness for behavioral interventions.

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges in the field of Bayesian deep learning, where it is not clear how to represent beliefs about a prediction task by prior distributions over model parameters. Bridging the fields of Bayesian deep learning and probabilistic meta-learning, we introduce a way to $\textit{learn}$ a weights prior from a collection of datasets by introducing a way to perform per-dataset amortised variational inference. The model we develop can be viewed as a neural process whose latent variable is the set of weights of a BNN and whose decoder is the neural network parameterised by a sample of the latent variable itself. This unique model allows us to study the behaviour of Bayesian neural networks under well-specified priors, use Bayesian neural networks as flexible generative models, and perform desirable but previously elusive feats in neural processes such as within-task minibatching or meta-learning under extreme data-starvation.

We give a randomized online algorithm that guarantees near-optimal $\widetilde O(\sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best bound of $\widetilde O(T^{2/3})$ and answers an open question of Fishelson et al. [2025b]. In addition, our algorithm is efficient: it runs in $\mathsf{poly}(T)$ time. A key technical idea we develop to obtain this result is to discretize the unit interval into bins at multiple scales of granularity and simultaneously use all scales to make randomized predictions, which we call multi-scale binning and may be of independent interest. A direct corollary of our result is an efficient online algorithm for minimizing the calibration error for general elicitable properties. This result does not require the Lipschitzness assumption of the identification function needed in prior work, making it applicable to median calibration, for which we achieve the first $\widetilde O(\sqrt T)$ calibration error guarantee.

Selecting interpretable feature sets in underdetermined ($n \ll p$) and highly correlated regimes constitutes a fundamental challenge in data science, particularly when analyzing physical measurements. In such settings, multiple distinct sparse subsets may explain the response equally well. Identifying these alternatives is crucial for generating domain-specific insights into the underlying mechanisms, yet conventional methods typically isolate a single solution, obscuring the full spectrum of plausible explanations. We present GEMSS (Gaussian Ensemble for Multiple Sparse Solutions), a variational Bayesian framework specifically designed to simultaneously discover multiple, diverse sparse feature combinations. The method employs a structured spike-and-slab prior for sparsity, a mixture of Gaussians to approximate the intractable multimodal posterior, and a Jaccard-based penalty to further control solution diversity. Unlike sequential greedy approaches, GEMSS optimizes the entire ensemble of solutions within a single objective function via stochastic gradient descent. The method is validated on a comprehensive benchmark comprising 128 synthetic experiments across classification and regression tasks. Results demonstrate that GEMSS scales effectively to high-dimensional settings ($p=5000$) with sample size as small as $n = 50$, generalizes seamlessly to continuous targets, handles missing data natively, and exhibits remarkable robustness to class imbalance and Gaussian noise. GEMSS is available as a Python package 'gemss' at PyPI. The full GitHub repository at https://github.com/kat-er-ina/gemss/ also includes a free, easy-to-use application suitable for non-coders.