Inference in non-linear continuous stochastic processes on trees is challenging, particularly when observations are sparse (leaf-only) and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general non-linear dynamics, while particle-based methods degrade in high dimensions. We propose Neural Backward Filtering Forward Guiding (NBFFG), a unified framework for both discrete transitions and continuous diffusions. Our method constructs a variational posterior by leveraging an auxiliary linear-Gaussian process. This auxiliary process yields a closed-form backward filter that serves as a ``guide'', steering the generative path toward high-likelihood regions. We then learn a neural residual--parameterized as a normalizing flow or a controlled SDE--to capture the non-linear discrepancies. This formulation allows for an unbiased path-wise subsampling scheme, reducing the training complexity from tree-size dependent to path-length dependent. Empirical results show that NBFFG outperforms baselines on synthetic benchmarks, and we demonstrate the method on a high-dimensional inference task in phylogenetic analysis with reconstruction of ancestral butterfly wing shapes.

Humans learn efficiently from their environment by engaging multiple interacting neural systems that support distinct yet complementary forms of control, including model-based (goal-directed) planning, model-free (habitual) responding, and episodic memory-based learning. Model-based mechanisms compute prospective action values using an internal model of the environment, supporting flexible but computationally costly planning; model-free mechanisms cache value estimates and build heuristics that enable fast, efficient habitual responding; and memory-based mechanisms allow rapid adaptation from individual experience. In this work, we aim to elucidate the computational principles underlying this biological efficiency and translate them into a sampling algorithm for scalable Bayesian inference through effective exploration of the posterior distribution. More specifically, our proposed algorithm comprises three components: a model-based module that uses the target distribution for guided but computationally slow sampling; a model-free module that uses previous samples to learn patterns in the parameter space, enabling fast, reflexive sampling without directly evaluating the expensive target distribution; and an episodic-control module that supports rapid sampling by recalling specific past events (i.e., samples). We show that this approach advances Bayesian methods and facilitates their application to large-scale statistical machine learning problems. In particular, we apply our proposed framework to Bayesian deep learning, with an emphasis on proper and principled uncertainty quantification.

Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a single feature remains challenging. We advance the state-of-the-art in diffusion models for tabular data with a cascaded approach. We first generate a low-resolution version of a tabular data row, that is, the collection of the purely categorical features and a coarse categorical representation of numerical features. Next, this information is leveraged in the high-resolution flow matching model via a novel guided conditional probability path and data-dependent coupling. The low-resolution representation of numerical features explicitly accounts for discrete outcomes, such as missing or inflated values, and therewith enables a more faithful generation of mixed-type features. We formally prove that this cascade tightens the transport cost bound. The results indicate that our model generates significantly more realistic samples and captures distributional details more accurately, for example, the detection score increases by 40%.

With the wide application of machine learning techniques in practice, privacy preservation has gained increasing attention. Protecting user privacy with minimal accuracy loss is a fundamental task in the data analysis and mining community. In this paper, we focus on regression tasks under $ε$-label differential privacy guarantees. Some existing methods for regression with $ε$-label differential privacy, such as the RR-On-Bins mechanism, discretized the output space into finite bins and then applied RR algorithm. To efficiently determine these finite bins, the authors rounded the original responses down to integer values. However, such operations does not align well with real-world scenarios. To overcome these limitations, we model both original and randomized responses as continuous random variables, avoiding discretization entirely. Our novel approach estimates an optimal interval for randomized responses and introduces new algorithms designed for scenarios where a prior is either known or unknown. Additionally, we prove that our algorithm, RPWithPrior, guarantees $ε$-label differential privacy. Numerical results demonstrate that our approach gets better performance compared with the Gaussian, Laplace, Staircase, and RRonBins, Unbiased mechanisms on the Communities and Crime, Criteo Sponsored Search Conversion Log, California Housing datasets.

We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate distributions $μ$ and $ν$ to a rank histogram on $\{ 0, \ldots, K\}$ and measure its deviation from uniformity via a discrete $f$-divergence, yielding a rank-statistic divergence estimator. We prove that the resulting estimator of the divergence is monotone in $K$, is always a lower bound of the true $f$-divergence, and we establish quantitative convergence rates for $K\to\infty$ under mild regularity of the quantile-domain density ratio. To handle high-dimensional data, we define the sliced rank-statistic $f$-divergence by averaging the univariate construction over random projections, and we provide convergence results for the sliced limit as well. We also derive finite-sample deviation bounds along with asymptotic normality results for the estimator. Finally, we empirically validate the approach by benchmarking against neural baselines and illustrating its use as a learning objective in generative modelling experiments.

Feature-based explanation methods aim to quantify how features influence the model's behavior, either locally or globally, but different methods often disagree, producing conflicting explanations. This disagreement arises primarily from two sources: how feature interactions are handled and how feature dependencies are incorporated. We propose GRANITE, a generalized regional explanation framework that partitions the feature space into regions where interaction and distribution influences are minimized. This approach aligns different explanation methods, yielding more consistent and interpretable explanations. GRANITE unifies existing regional approaches, extends them to feature groups, and introduces a recursive partitioning algorithm to estimate such regions. We demonstrate its effectiveness on real-world datasets, providing a practical tool for consistent and interpretable feature explanations.

The knowledge gradient is a popular acquisition function in Bayesian optimization (BO) for optimizing black-box objectives with noisy function evaluations. Many practical settings, however, allow only pairwise comparison queries, yielding a preferential BO problem where direct function evaluations are unavailable. Extending the knowledge gradient to preferential BO is hindered by its computational challenge. At its core, the look-ahead step in the preferential setting requires computing a non-Gaussian posterior, which was previously considered intractable. In this paper, we address this challenge by deriving an exact and analytical knowledge gradient for preferential BO. We show that the exact knowledge gradient performs strongly on a suite of benchmark problems, often outperforming existing acquisition functions. In addition, we also present a case study illustrating the limitation of the knowledge gradient in certain scenarios.

Self-supervised learning (SSL) -- a training paradigm in which models learn useful representations from unlabeled data by exploiting the data itself as a source of supervision -- has emerged as a foundational component of the recent success of transformer architectures. By avoiding the need for manual annotations, SSL retains many of the benefits traditionally associated with supervised learning while avoiding reliance on labeled data. Consequently, SSL is widely adopted as a pretraining paradigm for learning general-purpose representations that substantially accelerate the optimization of downstream tasks, especially in data-scarce settings. A canonical example of a self-supervised learning task is masked language modeling (MLM), in which a neural network is trained to predict masked tokens in text using the remaining tokens as contextual information (Devlin et al., 2019a; Howard and Ruder, 2018; Radford et al., 2018; Brown et al., 2020; OpenAI, 2024). For example, given the sentence "The capital of France is Paris", a typical MLM task would be to teach the model to infer that we are speaking about the capital of a country from the context "France" and "Paris" from the masked sentence "The [MASK] of France is Paris".

Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with the quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escaping stage, the high-variance but uninformative spike direction is multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this spike amplification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under broader anisotropic covariances.

We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second. This setting, which arises naturally in active learning and reweighting schemes, introduces intricate statistical dependencies across samples and fundamentally distinguishes the problem from classical single-stage ERM analyses. For linear models trained with a broad class of convex losses on Gaussian mixture data, we derive a sharp asymptotic characterization of the test error in the high-dimensional regime where the sample size and ambient dimension scale proportionally. Our results provide explicit, fully asymptotic predictions for the performance of the second-stage estimator despite the reuse of data and the presence of prediction-dependent losses. We apply this theory to revisit a well-studied pool-based active learning problem, removing oracle and sample-splitting assumptions made in prior work. We uncover a fundamental tradeoff in how the labeling budget should be allocated across stages, and demonstrate a double-descent behavior of the test error driven purely by data selection, rather than model size or sample count.