Stochastic gradient Markov chain Monte Carlo (SGMCMC) methods enable scalable Bayesian inference, but their performance depends strongly on hyperparameters such as the step size, mini-batch size, and number of leapfrog steps. Since most SGMCMC algorithms lack a Metropolis-Hastings acceptance rate, standard acceptance-based tuning methods are not directly applicable. We propose HyperMC, a multi-fidelity tuning framework that combines Hyperband-style resource allocation with kernel Stein discrepancy (KSD) evaluation. By running multiple successive-halving brackets, HyperMC balances broad exploration of a continuous hyperparameter space with increasingly accurate evaluation of promising configurations under a fixed computational budget. We further introduce Robust HyperMC, which uses global grid initialization followed by elite-guided local refinement to reduce sensitivity to random candidate generation and noisy finite-budget evaluations. Under suitable approximation and concentration conditions for the estimated KSD, we establish that the successive-halving component selects a near-optimal configuration among the sampled candidates with high probability and derive a sufficient computational budget for successful selection. Experiments on logistic regression, probabilistic matrix factorization, and Bayesian neural networks show that HyperMC improves posterior approximation or predictive calibration relative to MAMBA, grid search, and heuristic baselines, while Robust HyperMC yields more stable and reproducible tuning results.
WEASEL 2.0 is a dictionary-based time series classifier that combines dilated sliding windows with a randomised hyperparameter ensemble and a fixed-size dense feature representation. Two of its hyperparameter choices, the maximum ensemble size and the maximum window size, are specified by simple thresholding rules whose chosen thresholds are not empirically justified in the original paper. In this work we reproduce WEASEL 2.0 on 114 UCR datasets, achieving a mean accuracy of 0.865 and median of 0.928, closely matching the published values (Wilcoxon signed-rank, p = 0.655). We then test the sensitivity of four design choices: the downstream classifier, the absence of feature weighting, the maximum window-size rule, and the maximum ensemble-size rule. The first three are robust to perturbation. The fourth is over-provisioned for long-series datasets, motivating an adaptive rule that sets the maximum ensemble size from series length and number of classes. Evaluated on fixed-length datasets, the adaptive rule reduces peak fit memory by a median of 37 MB (mean 395 MB) and fit time by a median of 0.4 s (mean 4 s), with a median accuracy change of 0% (mean -0.11%). Memory and time savings concentrate on long-series datasets where the original rule allocates the largest ensemble size.
Nicholas Lourie, Kyunghyun Cho, Karen Ullrich +1cs.LG
Scaling laws promised cost-effective experiments; six years later, they have yet to fully deliver. Instead, researchers have found them unreliable at small scales (starting at 4M parameters) and concluded that sizable models cannot be avoided. We show this is not the case: the confounding factor is hyperparameters. Small models are highly sensitive, but hyperparameter sensitivity fades with scale. This small-scale sensitivity makes scaling laws easy to miss because they only emerge on the fully tuned frontier, and reaching that frontier requires an extensive search far beyond what most ever run. By ablating the basic scaling law recipe, we show well-tuned hyperparameters matter more than any other ingredient. Further, we reveal why those hyperparameters become easier to find: as scale increases, the hyperparameter loss surface becomes lower dimensional. Nevertheless while scaling laws exist in small models, extrapolation hits statistical limitations. A holistic approach is required. Synthesizing our insights with the recent literature, we develop a new methodology for model-centric research and demonstrate it on a question that once took the field years to settle: where to place normalization layers in the transformer architecture. From small-scale experiments, we recover the large scale result: pre-normalization works better as models grow in size. With the right tools and a better understanding, small-scale experiments can deliver on scaling laws' long-awaited promise.
Bayesian Optimization (BO) generally begins with an initialization phase: a batch of $n_0$ uninformed evaluations. The choice of $n_0$ remains largely heuristic, and we empirically observe that the total cost (random initial points plus BO iterations needed to find the global optimum) is U-shaped in $n_0$, i.e., a practitioner wastes resources by selecting either too low or too high a value of $n_0$. We find this tradeoff persists across MLE, Bayesian MCMC, and exact GP hyperparameters, as well as across acquisition functions. Toward the latter, Thompson Sampling appears an exception, with both total cost and simple regret essentially $n_0$-agnostic, though higher in our experiments. We attribute this U-shape to the known boundary issue of variance-driven BO: BO burns early budget on corners of the hypercube before turning inward. We demonstrate this effect using a 3D BO trajectory where the exact hyperparameters are known. We conclude with practical recommendations: use multi-step lookahead BO where possible; otherwise use Thompson Sampling when $n_0$ cannot be tuned, and a generously large $n_0$ when it can.
Background. Labeled data for security classification is scarce. Semi-supervised learning (SSL) propagates labels from a small labeled pool to larger unlabeled pools. Yet security applications often use SSL as a black box: default parameters, a fixed classifier, and no handling of pseudo-label-induced class imbalance. Aims. Recent work reports sizeable gains from optimizing SSL pipelines via joint search, AutoML, or per-component tuning. These gains are hard to attribute: they may reflect useful SSL-classifier interactions, or mostly from simply tuning the downstream classifier. We disentangle these effects for binary tabular security data with classical SSL and tree-based classifiers. Method. We build SemiScope as an analysis instrument, not a deployment recommendation. It uses Bayesian Optimization to jointly tune SSL settings, confidence filtering, oversampling, and the classifier. The key control, Tuned-Clf, fixes SSL to defaults but gets the same 100-trial classifier budget and validation-set threshold tuning as SemiScope. At 10% labels, we compare them with paired TOST using a +/-1.0 g-measure smallest effect of interest. Results. SemiScope beats every default SSL baseline on all five datasets, improving over the strongest by 0.7-12.7 points. Under the equal-budget control, Tuned-Clf is statistically equivalent to the full pipeline on 4 of 5 datasets; Phishing is inconclusive. Classifier HPO alone recovers a median 86% of SemiScope's gain over Default Self-Training (ST) + Random Forest (RF). Conclusions. The reusable contribution is the decomposition protocol. A simpler recipe suffices: use Self-Training, tune the classifier with Bayesian Optimization, and tune the decision threshold on validation data. It reaches within 1 g-measure of Supervised RF at 20-30% labels on four datasets and 40% on Drebin, at the same or lower label rate than Default ST + RF on every dataset.
Andrey A. Dukhovny, Andrey M. Langecs.LG cs.AI math.PR stat.ML
The number of trees is a central computational parameter in Random Forests: increasing it reduces finite-ensemble variability but increases training and prediction cost. Plateau-based tuning adapts this parameter through local comparisons of out-of-bag scores at a geometric triplet of tree counts. After the remaining hyperparameters have stabilized, however, the central triplet point need not converge to a deterministic value; instead, it fluctuates around a stationary regime. This paper develops a stationary-distribution theory for this process. The central ensemble size $B_t$ is modeled as a birth-death Markov chain on a geometric grid, and its stationary distribution is derived through local balance. Under a leading centered folded-normal approximation, equilibrium equations are obtained for the original update rule and a symmetric modified variant, implying that the stationary center $B_*=O(\varepsilon^{-2})$ as $\varepsilon\downarrow 0$. The stationary spread is also characterized. A local Gaussian approximation and a Fokker-Planck interpretation give grid-level variance constants. After conversion to the ensemble-size scale, $σ_{B,*}=O(\varepsilon^{-2})$, while the variance is $O(\varepsilon^{-4})$. The leading relative spread is independent of $\varepsilon$ and controlled by the scale factor and update rule. These results interpret plateau-based Random Forest tuning as a stochastic process rather than a deterministic stopping rule.
Hyperparameter selection is a critical step in the deployment of modern artificial intelligence systems, given the need to tune degrees of freedom such as inference-time parameters, implementation-level settings, and thresholds driving decision rules. Despite its practical importance, hyperparameter selection is typically performed using best-effort empirical methods such as grid search or Bayesian optimization, which provide no formal statistical guarantees on reliability or safety. This monograph presents a unified statistical framework for reliable hyperparameter selection, centered on the learn-then-test (LTT) paradigm, which formulates the problem as multiple hypothesis testing over a candidate set of hyperparameters. The framework enables the selection of hyperparameters that provably satisfy application-specific reliability requirements -- such as bounds on average risk, quantile risk, or information-theoretic constraints -- with explicit, finite-sample control of error probabilities. The supporting statistical machinery, namely p-values, e-values, and concentration inequalities, is developed from first principles in a dedicated appendix.
Yong Yi Bay, Kathleen A. Yearickcs.LG cs.AI math.NA stat.ML
Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolution G, exactly the Kolmogorov n-width of the smoothness class; the basis dimension is an explicit polynomial in G; and leave-one-out error follows from a single fit via the PRESS identity. Balancing the two known curves gives the minimizer analytically. We extend this calculus to many coordinates by replacing ambient input dimension with interaction order, the number of active low-order components in an ANOVA decomposition, yielding a scaling law in which the optimal resolution and error are power functions of the effective density (sample size per active component), with input dimension absent from the exponent. The law becomes an algorithm. KORE (Kolmogorov-optimal Order-aware Resolution Estimation) fits two pilot resolutions, solves a leverage-calibrated 2x2 system for the bias and noise scales, and evaluates the closed-form plug-in resolution with a tiny leave-one-out certificate: about a dozen fits instead of a full grid sweep, with a consistency guarantee as the sample grows. Across additive and sparse pairwise targets up to 80 input dimensions, KORE matches exhaustive 3-fold cross-validation and the full classical ladder (GCV, Mallows' Cp, AIC, BIC) while fitting roughly 8x fewer models; on 36 real tabular datasets it ranks first among 21 methods in accuracy per unit of compute, ahead of tuned boosters and kernel machines. When complexity lives in low interaction order, solving for the resolution beats searching for it.
Dictionary learning has long been studied from both optimization and probabilistic perspectives. While formulations with element-wise sparsity regularization (e.g., L1-based sparse coding) admit well-established probabilistic interpretations, many structured variants that impose global constraints lack a clear and tractable generative view. In this paper, we revisit a class of practically effective yet theoretically under-explored dictionary learning methods that impose a simple global regularization on the number of activated dictionary atoms, which we term parsimoniously activated dictionary learning (PADL). We show that PADL admits an equivalent formulation as maximum a posteriori estimation under a structured generative model, with auxiliary latent variables that govern global activation patterns. This formulation allows us to derive generalization guarantees that are difficult to obtain under the original formulation. More importantly, it yields an analytical characterization of the tradeoff between sparsity, storage cost, and reconstruction accuracy, enabling data-driven estimation of optimal hyperparameters. Based on this connection, we develop an efficient and interpretable PADL algorithm that eliminates manual hyperparameter tuning, achieving improved reconstruction performance under comparable sparsity levels on visual benchmarks. We further demonstrate its practical utility in accelerating inference for vision-language models.