arXiv subjects

Jakob Robnik

Publications and source records attributed to Jakob Robnik.

18 recordsLinked to original sources

arXiv2026

Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?

Scaling inference methods such as Markov chain Monte Carlo to high-dimensional models remains a central challenge in Bayesian deep learning. A promising recent proposal, microcanonical Langevin Monte Carlo, has shown state-of-the-art performance across a wide range of problems. However, its reliance on full-dataset gradients makes it prohibitively expensive for large-scale problems. This paper addresses a fundamental question: Can microcanonical dynamics effectively leverage mini-batch gradient noise? We provide the first systematic study of this problem, establishing a novel continuous-time theoretical analysis of stochastic-gradient microcanonical dynamics. We reveal two critical failure modes: a theoretically derived bias due to anisotropic gradient noise and numerical instabilities in complex high-dimensional posteriors. To tackle these issues, we propose a principled gradient noise preconditioning scheme shown to significantly reduce this bias and develop a novel, energy-variance-based adaptive tuner that automates step size selection and dynamically informs numerical guardrails. The resulting algorithm is a robust and scalable microcanonical Monte Carlo sampler that achieves state-of-the-art performance on challenging high-dimensional inference tasks like Bayesian neural networks. Combined with recent ensemble techniques, our work unlocks a new class of stochastic microcanonical Langevin ensemble (SMILE) samplers for large-scale Bayesian inference.

cs.LG↗

arXiv2026

Exoplanet transit search at the detection limit: detection and false alarm vetting pipeline

One of the primary mission goals of the Kepler space telescope was to detect Earth-like terrestrial planets in the habitable zone around Sun-like stars. These planets are at the detection limit, where the Kepler detection and vetting pipeline produced unreliable planet candidates. We present a novel pipeline that improves the removal of localized defects prior to the planet search, improves vetting at the level of individual transits and introduces a Bayes factor test statistic and an algorithm for extracting multiple candidates from a single detection run. We show with injections in the Kepler data that the introduced novelties improve pipeline's completeness at a fixed false alarm rate. We apply the pipeline to the stars with previously identified planet candidates and show that our pipeline successfully recovers the previously confirmed candidates, but flags a considerable portion of unconfirmed candidates as likely false alarms, especially in the long period, low signal-to-noise ratio regime. In particular, several known Earth-like candidates in the habitable zone, such as KOI 8063.01, 8107.01 and 8242.01, are identified as false alarms, which could have a significant impact on the estimates of $η_{\oplus}$, i.e., the occurrence of Earth-like planets in the habitable zone.

astro-ph.EP↗

arXiv2026

Radiological mapping and uncertainty quantification by a fast Microcanonical Langevin Monte Carlo sampler

Radiological mapping plays a critical role in nuclear emergency response and environmental management activities. A radiation image, representing the spatial and intensity distribution of the radioactivity, is reconstructed from the radiation data and the associated contextual information. Typical image reconstruction methods, such as Maximum Likelihood Expectation-Maximization (ML-EM), only provide point estimates of the pixel or voxel activities without associated uncertainties. Here, we apply a new Microcanonical Langevin Monte Carlo (MCLMC) sampler for radiation image reconstruction and uncertainty quantification. The MCLMC sampler properties are first tested with synthetic radiation images. Methods to obtain the radiation distribution estimate and the associated uncertainty from the samples drawn by MCLMC are discussed. Given sufficient measurement statistics, the radiation distribution estimate obtained from MCLMC results closely resembles the ground truth with less risk of over- or under-fitting compared to ML-EM. When MCLMC is run in parallel on a GPU, the samples can converge to the posterior distribution in about 10 seconds for an image with $10^3$--$10^4$ pixels, which is significantly faster than other comparable Markov Chain Monte Carlo (MCMC) samplers. We also tested MCLMC on a dataset from a real distributed source radiological mapping campaign, and the reconstructed results agree well with ground truth. The fast MCLMC sampler therefore enables improved imaging accuracy and prompt uncertainty quantification for reconstructed radiation images, which can better inform decision-making in response to radiological events.

physics.med-ph↗

arXiv2026

Faster parallel MCMC: Metropolis adjustment is best served warm

Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can significantly speed up MCMC inference by running a large number of chains in parallel, each collecting a single sample. However, the parallel approach converges slowly if the chains are not initialized close to the target distribution (cold start). Theoretically this can be resolved by initially running MCMC without Metropolis-Hastings adjustment to quickly converge to the vicinity of the target distribution and then turn on adjustment to achieve fine convergence. However, no practical scheme uses this strategy, due to the difficulty of automatically selecting the step size during the unadjusted phase. We here develop Late Adjusted Parallel Sampler (LAPS), which is precisely such a scheme and is applicable out of the box, all the hyperparameters are selected automatically. LAPS takes advantage of ensemble-based hyperparameter adaptation to estimate the bias at each iteration and converts it to the appropriate step size. We show that LAPS consistently and significantly outperforms ensemble adjusted methods such as MEADS or ChESS and the optimization-based initializer Pathfinder on a variety of standard benchmark problems. LAPS typically achieves two orders of magnitude lower wall-clock time than the corresponding sequential algorithms such as NUTS.

stat.CO↗

arXiv2025

Reassessment of Kepler's habitable zone Earth-like exoplanets with data-driven null-signal templates

One of the primary mission goals of the Kepler space telescope is to detect Earth-like terrestrial planets in the habitable zone around Sun-like stars. Unfortunately, such planets are at the detection limit. Estimating their statistical significance via false alarm probability (FAP) is crucial for their validation, and has a large impact on the estimate of their occurrence rate, which is of central importance for future spectroscopic missions searching for life signatures. Current methods estimate FAP by light curve inverting or scrambling, but we show that both of these approaches are unsatisfactory. Here we propose to modify the planet transit template by randomly shifting the transit times by small amounts. We show that the exoplanet search with the resulting Null Signal Template (NST) has the same statistical properties as with the true periodic template, which enables assigning a reliable star-specific FAP to every candidate. We show on simulations and on the real data that the method is robust to unmodeled noise contamination. We reevaluate the statistical significance of all 47 previously proposed habitable Earth-like and super Earth Kepler candidates and assign them star-specific NST based FAP. We identify 29 candidates with FAP below 1%, 7 of whom are currently not considered confirmed. Among these are Kepler 452b with radius $1.5 R{\oplus}$, a period of 384 days, and KOI 2194.03 with radius $1.8 R{\oplus}$ and a period of 445 days, both around Sun-like G stars. Several well-known candidates should be considered marginal or likely false alarms, including Kepler 186f with 20% FAP.

astro-ph.EP↗

arXiv2025

Metropolis Adjusted Microcanonical Hamiltonian Monte Carlo

Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a very large number of parameters or a complicated geometry. Microcanonical Langevin Monte Carlo (MCLMC) has been recently proposed as an alternative which shows striking gains in efficiency over NUTS, especially for high-dimensional problems. However, it produces biased samples, with a bias that is hard to control in general. We introduce the Metropolis-Adjusted Microcanonical sampler (MAMS), which relies on the same dynamics as MCLMC, but introduces a Metropolis-Hastings step and thus produces asymptotically unbiased samples. We develop an automated tuning scheme for the hyperparameters of the algorithm, making it applicable out of the box. We demonstrate that MAMS outperforms NUTS across the board on benchmark problems of varying complexity and dimensionality, achieving up to a factor of seven speedup.

stat.CO↗

arXiv2025

Fluctuation without dissipation: Microcanonical Langevin Monte Carlo

Stochastic sampling algorithms such as Langevin Monte Carlo are inspired by physical systems in a heat bath. Their equilibrium distribution is the canonical ensemble given by a prescribed target distribution, so they must balance fluctuation and dissipation as dictated by the fluctuation-dissipation theorem. In contrast to the common belief, we show that the fluctuation-dissipation theorem is not required because only the configuration space distribution, and not the full phase space distribution, needs to be canonical. We propose a continuous-time Microcanonical Langevin Monte Carlo (MCLMC) as a dissipation-free system of stochastic differential equations (SDE). We derive the corresponding Fokker-Planck equation and show that the stationary distribution is the microcanonical ensemble with the desired canonical distribution on configuration space. We prove that MCLMC is ergodic for any nonzero amount of stochasticity, and for smooth, convex potentials, the expectation values converge exponentially fast. Furthermore, the deterministic drift and the stochastic diffusion separately preserve the stationary distribution. This uncommon property is attractive for practical implementations as it implies that the drift-diffusion discretization schemes are bias-free, so the only source of bias is the discretization of the deterministic dynamics. We applied MCLMC on a lattice $ϕ^4$ model, where Hamiltonian Monte Carlo (HMC) is currently the state-of-the-art integrator. For the same accuracy, MCLMC converges 12 times faster than HMC on an $8\times8$ lattice. On a $64\times64$ lattice, it is already 32 times faster. The trend is expected to persist to larger lattices, which are of particular interest, for example, in lattice quantum chromodynamics.

hep-lat↗

arXiv2025

Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networks

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.

cs.LG↗

arXiv2024

Practical and Scalable Hamiltonian Monte Carlo Without the Metropolis Test

Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are leading methods for sampling from high-dimensional distributions with differentiable densities. Both rely on numerical integration, which introduces asymptotic bias in expectation estimates. This bias can be removed by adjusting the numerical integration with a Metropolis Hastings (MH) step, at a cost of slower mixing and larger variance. Alternatively, we can trade bias for lower variance if we avoid the MH step and use an appropriate step size of integration. These unadjusted schemes have strong performance, especially in high-dimensional problems, but are rarely used due to the lack of automated step size selection. We propose an automatic tuning scheme that selects a step size to meet a user-specified asymptotic bias tolerance. The method is based on a relationship between energy error and bias which we establish. We rigorously analyze the method in the Gaussian setting and numerically extend the analysis to several non Gaussian problems. Experiments on Bayesian inference and large scale statistical physics models (with over one million parameters) show that, with our tuning, unadjusted methods consistently and significantly outperform adjusted counterparts.

stat.CO↗

arXiv2024

Periodicity significance testing with null-signal templates: reassessment of PTF's SMBH binary candidates

Periodograms are widely employed for identifying periodicity in time series data, yet they often struggle to accurately quantify the statistical significance of detected periodic signals when the data complexity precludes reliable simulations. We develop a data-driven approach to address this challenge by introducing a null-signal template (NST). The NST is created by carefully randomizing the period of each cycle in the periodogram template, rendering it non-periodic. It has the same frequentist properties as a periodic signal template regardless of the noise probability distribution, and we show with simulations that the distribution of false positives is the same as with the original periodic template, regardless of the underlying data. Thus, performing a periodicity search with the NST acts as an effective simulation of the null (no-signal) hypothesis, without having to simulate the noise properties of the data. We apply the NST method to the supermassive black hole binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi et al. had previously proposed 33 high signal to (white) noise candidates utilizing simulations to quantify their significance. Our approach reveals that these simulations do not capture the complexity of the real data. There are no statistically significant periodic signal detections above the non-periodic background. To improve the search sensitivity we introduce a Gaussian quadrature based algorithm for the Bayes Factor with correlated noise as a test statistic, in contrast to the standard signal to white noise. We show with simulations that this improves sensitivity to true signals by more than an order of magnitude. However, using the Bayes Factor approach also results in no statistically significant detections in the PTF data.

astro-ph.GA↗

arXiv2022

Microcanonical Hamiltonian Monte Carlo

We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models which follow a fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels. MCHMC tunes the Hamiltonian function such that the marginal of the uniform distribution on the constant-energy-surface over the momentum variables gives the desired target distribution. We show that MCHMC requires occasional energy conserving billiard-like momentum bounces for ergodicity, analogous to momentum resampling in HMC. We generalize the concept of bounces to a continuous version with partial direction preserving bounces at every step, which gives an energy conserving underdamped Langevin-like dynamics with non-Gaussian noise (MCLMC). MCHMC and MCLMC exhibit favorable scalings with condition number and dimensionality. We develop an efficient hyperparameter tuning scheme that achieves high performance and consistently outperforms NUTS HMC on several standard benchmark problems, in some cases by more than an order of magnitude.

stat.CO↗

arXiv2022

Statistical significance testing for mixed priors: a combined Bayesian and frequentist analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam's razor via multiplicity or trials factor in the Look Elsewhere Effect. However, if the prior is not known completely, the frequentist hypothesis test via the false positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey's prior. We also show that mixed priors increase the statistical power in frequentist analyses over the likelihood ratio test statistic. We develop an analytic formalism that does not require expensive simulations using a statistical mechanics approach to hypothesis testing in Bayesian and frequentist statistics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as energy versus entropy competition. We present analytic expressions that generalize Wilks' theorem beyond its usual regime of validity and work in a non-asymptotic regime. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than $10^7$. We show that our analytic expressions reproduce the p-values derived from numerical simulations.

physics.data-an↗

arXiv2021

Self-Calibrating the Look-Elsewhere Effect: Fast Evaluation of the Statistical Significance Using Peak Heights

In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. This paper introduces a method to calibrate the false alarm probability (FAP), or $p$-value, for a given dataset by considering the heights of the highest peaks in the likelihood. In the simplest form of self-calibration, the look-elsewhere-corrected $χ^2$ of a physical peak is approximated by the $χ^2$ of the peak minus the $χ^2$ of the highest noise-induced peak. Generalizing this concept to consider lower peaks provides a fast method to quantify the statistical significance with improved accuracy. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology.

astro-ph.IM↗

arXiv2021

Through a Black Hole into a New Universe

We show that an S-Brane which arises in the inside of the black hole horizon when the Weyl curvature reaches the string scale induces a continuous transition between the inside of the black hole and the beginning of a new universe. This provides a simultaneous resolution of both the black hole and Big Bang singularities. In this context, the black hole information loss problem is also naturally resolved.

hep-th↗

arXiv2021

Matched filtering with non-Gaussian noise for planet transit detections

We develop a method for planet detection in transit data, which is based on the Matched Filter technique, combined with the Gaussianization of the noise outliers. The method is based on Fourier transforms and is as fast as the existing methods for planet searches. The Gaussinized Matched Filter (GMF) method significantly outperforms the standard baseline methods in terms of the false positive rate, enabling planet detections at up to 30 % lower transit amplitudes. Moreover, the method extracts all the main planet transit parameters, amplitude, period, phase, and duration. By comparison to the state of the art Gaussian Process methods on both simulations and real data we show that all the transit parameters are determined with an optimal accuracy (no bias and minimum variance), meaning that the GMF method can be used both for the initial planet detection and the follow-up planet parameter analysis.

astro-ph.EP↗

arXiv2021

Low-Energy String Theory Predicts Black Holes Hide a New Universe

We propose a construction with which to resolve the black hole singularity and enable an anisotropic cosmology to emerge from the inside of the hole. The model relies on the addition of an S-brane to the effective action which describes the geometry of space-time. This space-like defect is located inside of the horizon on a surface where the Weyl curvature reaches a limiting value. We study how metric fluctuations evolve from the outside of the black hole to the beginning of the cosmological phase to the future of the S-brane. Our setup addresses i) the black hole singularity problem, ii) the cosmological singularity problem and iii) the information loss paradox since the outgoing Hawking radiation is entangled with the state inside the black hole which becomes the new universe.

hep-th↗

arXiv2020

Kepler-90: Giant transit-timing variations reveal a super-puff

Exoplanet Transit Timing Variations (TTVs) caused by gravitational forces between planets can be used to determine planetary masses and orbital parameters. Most of the observed TTVs are small and sinusoidal in time, leading to degeneracies between the masses and orbital parameters. Here we report a TTV analysis of Kepler-90g and Kepler-90h, which exhibit large TTVs up to 25 hours. With optimization, we find a unique solution which allows us to constrain all of the orbital parameters. The best fit masses for Kepler-90g and 90h are $15.0^{+0.9}_{-0.8}$ $M_{\bigoplus}$ (Earth mass) and $203^{+5}_{-5}M_{\bigoplus}$, respectively, with Kepler-90g having an unusually low apparent density of $0.15\pm 0.05\, {\rm g\,cm^{-3}}$. The uniqueness of orbital parameter solution enables a long-term dynamical integration, which reveals that although their periods are close to 2:3 orbital resonance, they are not locked in resonance, and the configuration is stable over billions of years. The dynamical history of the system suggests that planet interactions are able to raise the eccentricities and break the resonant lock after the initial formation.

astro-ph.EP↗

arXiv2019

Kepler data analysis: non-Gaussian noise and Fourier Gaussian process analysis of star variability

We develop a statistical analysis model of Kepler star flux data in the presence of planet transits, non-Gaussian noise, and star variability. We first develop a model for Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue these components need to be modeled together if optimal signal is to be extracted from the data. For the star variability model we develop an optimal Gaussian process analysis using a Fourier based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the star variability than the standard spline method, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than the standard spline method.

astro-ph.EP↗