We revisit the classic ski rental problem through the lens of Bayesian decision-making and machine-learned predictions. While traditional algorithms minimize worst-case cost without assumptions, and recent learning-augmented approaches leverage noisy forecasts with robustness guarantees, our work unifies these perspectives. We propose a discrete Bayesian framework that maintains exact posterior distributions over the time horizon, enabling principled uncertainty quantification and seamless incorporation of expert priors. Our algorithm achieves prior-dependent competitive guarantees and gracefully interpolates between worst-case and fully-informed settings. Our extensive experimental evaluation demonstrates superior empirical performance across diverse scenarios, achieving near-optimal results under accurate priors while maintaining robust worst-case guarantees. This framework naturally extends to incorporate multiple predictions, non-uniform priors, and contextual information, highlighting the practical advantages of Bayesian reasoning in online decision problems with imperfect predictions.

Random telegraph noise is a prevalent variability phenomenon in nanoelectronic devices, arising from stochastic carrier exchange at defect sites and critically impacting device reliability and performance. Conventional analysis techniques often rely on restrictive assumptions or manual interventions, limiting their applicability to complex, noisy datasets. Here, we introduce RTNinja, a generalized, fully automated machine learning framework for the unsupervised analysis of random telegraph noise signals. RTNinja deconvolves complex signals to identify the number and characteristics of hidden individual sources without requiring prior knowledge of the system. The framework comprises two modular components: LevelsExtractor, which uses Bayesian inference and model selection to denoise and discretize the signal, and SourcesMapper, which infers source configurations through probabilistic clustering and optimization. To evaluate performance, we developed a Monte Carlo simulator that generates labeled datasets spanning broad signal-to-noise ratios and source complexities; across 7000 such datasets, RTNinja consistently demonstrated high-fidelity signal reconstruction and accurate extraction of source amplitudes and activity patterns. Our results demonstrate that RTNinja offers a robust, scalable, and device-agnostic tool for random telegraph noise characterization, enabling large-scale statistical benchmarking, reliability-centric technology qualification, predictive failure modeling, and device physics exploration in next-generation nanoelectronics.

Our bound does not require the prior to have any parametric form.

To derive lower bounds, we use tools from information theory (e.g., Shtarkov sum),

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly through the connection to PAC-Bayes analysis. A second line of work has provided algorithm-specific generalization bounds through stability arguments or using mutual information bounds, and has shown that the bounds are tight in practice, but unfortunately these bounds do not directly apply to approximate Bayesian algorithms. This paper fills this gap by developing algorithm-specific stability based generalization bounds for a class of approximate Bayesian algorithms that includes VI, specifically when using stochastic gradient descent to optimize their objective. As in the non-Bayesian case, the generalization error is bounded by by expected parameter differences on a perturbed dataset. The new approach complements PAC-Bayes analysis and can provide tighter bounds in some cases. An experimental illustration shows that the new approach yields non-vacuous bounds on modern neural network architectures and datasets and that it can shed light on performance differences between variant approximate Bayesian algorithms.

In this paper, we propose an optimized Transformer model that integrates Bayesian algorithms with a Bidirectional Gated Recurrent Unit (BiGRU), and apply it to fake news classification for the first time. First, we employ the TF-IDF method to extract features from news texts and transform them into numeric representations to facilitate subsequent machine learning tasks. Two sets of experiments are then conducted for fake news detection and classification: one using a Transformer model optimized only with BiGRU, and the other incorporating Bayesian algorithms into the BiGRU-based Transformer. Experimental results show that the BiGRU-optimized Transformer achieves 100% accuracy on the training set and 99.67% on the test set, while the addition of the Bayesian algorithm maintains 100% accuracy on the training set and slightly improves test-set accuracy to 99.73%. This indicates that the Bayesian algorithm boosts model accuracy by 0.06%, further enhancing the detection capability for fake news. Moreover, the proposed algorithm converges rapidly at around the 10th training epoch with accuracy nearing 100%, demonstrating both its effectiveness and its fast classification ability. Overall, the optimized Transformer model, enhanced by the Bayesian algorithm and BiGRU, exhibits excellent continuous learning and detection performance, offering a robust technical means to combat the spread of fake news in the current era of information overload.

We study a mistake-driven variant of an on-line Bayesian learn(cid:173) ing algorithm (similar to one studied by Cesa-Bianchi, Helmbold, and Panizza [CHP96]). This variant only updates its state (learns) on trials in which it makes a mistake. The algorithm makes binary classifications using a linear-threshold classifier and runs in time lin(cid:173) ear in the number of attributes seen by the learner. We have been able to show, theoretically and in simulations, that this algorithm performs well under assumptions quite different from those embod(cid:173) ied in the prior of the original Bayesian algorithm. It can handle situations that we do not know how to handle in linear time with Bayesian algorithms.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) per- form favorably when compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algo- rithms' modeling assumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (us- ing logloss), our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

In a variety of behavioral tasks, subjects exhibit an automatic and apparently sub-optimal sequential effect: they respond more rapidly and accurately to a stimulus if it reinforces a local pattern in stimulus history, such as a string of repetitions or alternations, compared to when it violates such a pattern. This is often the case even if the local trends arise by chance in the context of a randomized design, such that stimulus history has no predictive power. In this work, we use a normative Bayesian framework to examine the hypothesis that such idiosyncrasies may reflect the inadvertent engagement of fundamental mechanisms critical for adapting to changing statistics in the natural environment. We show that prior belief in non-stationarity can induce experimentally observed sequential effects in an otherwise Bayes-optimal algorithm. The Bayesian algorithm is shown to be well approximated by linear-exponential filtering of past observations, a feature also apparent in the behavioral data.