机器学习

We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator…

Scaling laws for neural networks, in which the loss decays as a power-law in the number of parameters, data, and compute, depend fundamentally on the spectral structure of the data covariance, with power-law eigenvalue decay appearing…

In this paper, we analyze the two time-scale stochastic approximation (TTSSA) algorithm introduced in Borkar (1997) using a martingale approach. This approach leads to simple sufficient conditions for the iterations to be bounded almost…

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…

AI systems increasingly assist human decision making by producing preliminary assessments of complex inputs. However, such AI-generated assessments can often be noisy or systematically biased, raising a central question: how should costly…

Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry…

Square-root Kalman filters propagate state covariances in Cholesky-factor form for numerical stability, and are a natural target for gradient-based parameter learning in state-space models. Their core operation, triangularization of a…

We introduce Holographic Invariant Storage (HIS), a protocol that assembles known properties of bipolar Vector Symbolic Architectures into a design-time safety contract for LLM context-drift mitigation. The contract provides three…

Asynchronous Bayesian optimization is widely used for gradient-free optimization in domains with independent parallel experiments and varying evaluation times. Existing methods posit that standard acquisitions lead to redundant and repeated…

We introduce the Integrated Tsallis Combination (ITC), a hybrid impurity measure for decision tree learning that combines normalized Tsallis entropy with an exponential polarization component. While many existing measures sacrifice…

We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…

We introduce structural causal bottleneck models (SCBMs), a novel class of structural causal models. At the core of SCBMs lies the assumption that causal effects between high-dimensional variables only depend on low-dimensional summary…

While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…

We propose a method for transfer learning in nonparametric regression using a random forest (RF) with distance covariance-based feature weights, assuming the unknown source and target regression functions are sparsely different. Our method…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Feature importance (FI) measures are widely used to assess the contributions of predictors to an outcome, but they may target different notions of relevance. When predictors are correlated, traditional statistical FI methods are often…

The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In…

We consider the problem of statistical inference when the data is collected via a Thompson Sampling-type algorithm. While Thompson Sampling (TS) is known to be both asymptotically optimal and empirically effective, its adaptive sampling…

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…

The Transfer Elastic Net is an estimation method for linear regression models that combines $\ell_1$ and $\ell_2$ norm penalties to facilitate knowledge transfer. In this study, we derive a non-asymptotic $\ell_2$ norm estimation error…