arXiv subjects

Sinan Yıldırım

Publications and source records attributed to Sinan Yıldırım.

14 recordsLinked to original sources

arXiv2026

Combining Homomorphic Encryption and Differential Privacy in Federated Learning for Model Inspection and Availability

The increasing prevalence of decentralized data has led to a growing interest in federated learning, which enables collaborative model training without clients sharing their sensitive local data. However, FL alone does not sufficiently protect sensitive training data and is generally coupled with privacy-preserving techniques, such as differential privacy and homomorphic encryption. Although powerful, these techniques address separate concerns via different mechanisms, so relying on just one might prove insufficient or impractical for addressing challenges associated with federated learning. In this work, we propose a privacy-preserving federated learning framework that combines homomorphic encryption-based training with differential privacy-based model inspection and release. We adopt a Markov chain Monte Carlo-based Bayesian privacy estimation method to estimate the privacy of our proposed framework. Our results show that this method improves both model utility and estimated privacy over the baseline method that relies solely on differential privacy for training. In our experiments with the FEMNIST dataset, by the end of training, our method reaches a test loss of $1.09$, compared to $2.37$ for the differential privacy-only approach, while providing stronger estimated privacy protection, with the estimated posterior mean of the privacy parameter $ε$ of $4.32$, compared to $7.26$ for the differential privacy-only approach. We also show that intermittent model monitoring can preserve the encrypted training trajectory while, under our evaluated experimental setting, providing estimated privacy comparable to or stronger than the differential privacy-only approach.

cs.CR↗

arXiv2026

The Quick and the Dead: Estimating Sparse-Matrix Permanents with Adaptive Work Filtering

Rasmussen's permanent estimator is a simple and unbiased estimator for the permanent of a binary matrix, but its practical performance can be limited by trajectories that terminate before completing a perfect matching. These failed trajectories, together with dispersion among the surviving weights, can substantially reduce the effective sample size. Although the literature leverages techniques such as matrix scaling to improve proposal balance and support filtering to remove structurally infeasible choices, using these at every step can substantially increase the trajectory cost. Furthermore, they do not directly address the choice of the next vertex. This paper uses the classical minimum-degree ordering in sparse matrix algorithms to select the next vertex with O(n + m) total bucket-maintenance work per trajectory, where n is the number of rows/columns in the matrix and m is the number of nonzeros. The proposed estimator uses adaptive schedules to invoke the more expensive scaling and filtering operations only when needed. The experiments show that it is competitive with the state of the art on the tested small matrices and scales effectively to large sparse matrices.

cs.DS↗

arXiv2026

Bayesian Membership Privacy for Graph Neural Networks

Existing privacy analyses for Graph Neural Networks (GNNs) largely inherit assumptions from non-graph settings, overlooking structural correlations and stochastic training-graph sampling. In particular, node-dependent priors make type-I and type-II errors alone insufficient to characterize the best membership inference test. To address this, we introduce Bayesian Membership Privacy (BMP), a sampling-aware formulation of node-level membership privacy that incorporates node-dependent priors and treats graph sampling probabilities as part of the adversary's knowledge. BMP casts membership inference as a Bayesian hypothesis test and accordingly quantifies membership privacy in terms of posterior membership probability. We explore theoretical properties of BMP in relation to the existing definitions in the literature. We further propose a practical, sampling-aware auditing mechanism to estimate the parameters of BMP as a measure of node-level privacy leakage in GNNs. We conduct experiments on benchmark graph datasets and show that BMP yields fine-grained privacy insights that are not visible through global attack accuracy alone.

cs.CR↗

arXiv2026

Learning with Subset Stacking

We propose a new regression algorithm that learns from a set of input-output pairs. Our algorithm is designed for populations where the relation between the input variables and the output variable exhibits a heterogeneous behavior across the predictor space. The algorithm starts with generating subsets that are concentrated around random points in the input space. This is followed by training a local predictor for each subset. Those predictors are then combined in a novel way to yield an overall predictor. We call this algorithm "LEarning with Subset Stacking" or LESS, due to its resemblance to the method of stacking regressors. We offer bagging and boosting variants of LESS and test against the state-of-the-art methods on several datasets. Our comparison shows that LESS is highly competitive.

cs.LG↗

arXiv2025

Privacy of SGD under Gaussian or Heavy-Tailed Noise: Guarantees without Gradient Clipping

The injection of heavy-tailed noise into the iterates of stochastic gradient descent (SGD) has garnered growing interest in recent years due to its theoretical and empirical benefits for optimization and generalization. However, its implications for privacy preservation remain largely unexplored. Aiming to bridge this gap, we provide differential privacy (DP) guarantees for noisy SGD, when the injected noise follows an $α$-stable distribution, which includes a spectrum of heavy-tailed distributions (with infinite variance) as well as the light-tailed Gaussian distribution. Considering the $(ε, δ)$-DP framework, we show that SGD with heavy-tailed perturbations achieves $(0, O(1/n))$-DP for a broad class of loss functions which can be non-convex, where $n$ is the number of data points. As a remarkable byproduct, contrary to prior work that necessitates bounded sensitivity for the gradients or clipping the iterates, our theory can handle unbounded gradients without clipping, and reveals that under mild assumptions, such a projection step is not actually necessary. Our results suggest that, given other benefits of heavy-tails in optimization, heavy-tailed noising schemes can be a viable alternative to their light-tailed counterparts.

stat.ML↗

arXiv2023

Differentially Private Distributed Bayesian Linear Regression with MCMC

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

stat.ML↗

arXiv2023

Energy Optimization of Wind Turbines via a Neural Control Policy Based on Reinforcement Learning Markov Chain Monte Carlo Algorithm

This study focuses on the numerical analysis and optimal control of vertical-axis wind turbines (VAWT) using Bayesian reinforcement learning (RL). We specifically address small-scale wind turbines, which are well-suited to local and compact production of electrical energy on a small scale, such as urban and rural infrastructure installations. Existing literature concentrates on large scale wind turbines which run in unobstructed, mostly constant wind profiles. However urban installations generally must cope with rapidly changing wind patterns. To bridge this gap, we formulate and implement an RL strategy using the Markov chain Monte Carlo (MCMC) algorithm to optimize the long-term energy output of a wind turbine. Our MCMC-based RL algorithm is a model-free and gradient-free algorithm, in which the designer does not have to know the precise dynamics of the plant and its uncertainties. Our method addresses the uncertainties by using a multiplicative reward structure, in contrast with additive reward used in conventional RL approaches. We have shown numerically that the method specifically overcomes the shortcomings typically associated with conventional solutions, including, but not limited to, component aging, modeling errors, and inaccuracies in the estimation of wind speed patterns. Our results show that the proposed method is especially successful in capturing power from wind transients; by modulating the generator load and hence the rotor torque load, so that the rotor tip speed quickly reaches the optimum value for the anticipated wind speed. This ratio of rotor tip speed to wind speed is known to be critical in wind power applications. The wind to load energy efficiency of the proposed method was shown to be superior to two other methods; the classical maximum power point tracking method and a generator controlled by deep deterministic policy gradient (DDPG) method.

eess.SY↗

arXiv2023

Differentially Private Online Bayesian Estimation With Adaptive Truncation

We propose a novel online and adaptive truncation method for differentially private Bayesian online estimation of a static parameter regarding a population. We assume that sensitive information from individuals is collected sequentially and the inferential aim is to estimate, on-the-fly, a static parameter regarding the population to which those individuals belong. We propose sequential Monte Carlo to perform online Bayesian estimation. When individuals provide sensitive information in response to a query, it is necessary to perturb it with privacy-preserving noise to ensure the privacy of those individuals. The amount of perturbation is proportional to the sensitivity of the query, which is determined usually by the range of the queried information. The truncation technique we propose adapts to the previously collected observations to adjust the query range for the next individual. The idea is that, based on previous observations, we can carefully arrange the interval into which the next individual's information is to be truncated before being perturbed with privacy-preserving noise. In this way, we aim to design predictive queries with small sensitivity, hence small privacy-preserving noise, enabling more accurate estimation while maintaining the same level of privacy. To decide on the location and the width of the interval, we use an exploration-exploitation approach a la Thompson sampling with an objective function based on the Fisher information of the generated observation. We show the merits of our methodology with numerical examples.

cs.LG↗

arXiv2020

Metropolis-Hastings with Averaged Acceptance Ratios

Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $π$ defined on a space $(Θ,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{θ_{n},n\geq1\}$ of invariant distribution $π$ and such that the distribution of $θ_{i}$ converges to $π$ as $i\rightarrow\infty$. In practice one is typically interested in the computation of expectations of functions, say $f$, with respect to $π$ and it is also required that averages $M^{-1}\sum_{n=1}^{M}f(θ_{n})$ converge to the expectation of interest. The iterative nature of MCMC makes it difficult to develop generic methods to take advantage of parallel computing environments when interested in reducing time to convergence. While numerous approaches have been proposed to reduce the variance of ergodic averages, including averaging over independent realisations of $\{θ_{n},n\geq1\}$ simulated on several computers, techniques to reduce the "burn-in" of MCMC are scarce. In this paper we explore a simple and generic approach to improve convergence to equilibrium of existing algorithms which rely on the Metropolis-Hastings (MH) update, the main building block of MCMC. The main idea is to use averages of the acceptance ratio w.r.t. multiple realisations of random variables involved, while preserving $π$ as invariant distribution. The methodology requires limited change to existing code, is naturally suited to parallel computing and is shown on our examples to provide substantial performance improvements both in terms of convergence to equilibrium and variance of ergodic averages. In some scenarios gains are observed even on a serial machine.

stat.CO↗

arXiv2018

Scalable Monte Carlo inference for state-space models

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in \citet{Andrieu_et_al_2010} and presents several practical advantages over standard approaches. The ratio is estimated using a unique source of randomness instead of estimating separately the two likelihood terms involved. Beyond the benefits in terms of variance reduction one may expect in general from this type of approach, an important point here is that the variance of this estimator decreases as the distance between the likelihood parameters decreases. We show how this can be exploited in the context of Monte Carlo Markov chain (MCMC) algorithms, leading to the development of a new class of exact-approximate MCMC methods to perform Bayesian static parameter inference in state-space models. We show through simulations that, in contrast to the Particle Marginal Metropolis-Hastings (PMMH) algorithm of Andrieu_et_al_2010, the computational effort required by this novel MCMC scheme scales very favourably for large data sets.

stat.ME↗

arXiv2018

On the utility of Metropolis-Hastings with asymmetric acceptance ratio

The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $π$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such an evaluation is impossible, and yet are guaranteed to sample from $π$ asymptotically. The most popular approach to have emerged is arguably the pseudo-marginal MH algorithm which substitutes an unbiased estimate of an unnormalised version of $π$ for $π$. Alternative pseudo-marginal algorithms relying instead on unbiased estimates of the MH acceptance ratio have also been proposed. These algorithms can have better properties than standard PM algorithms. Convergence properties of both classes of algorithms are known to depend on the variability of the estimators involved and reduced variability is guaranteed to decrease the asymptotic variance of ergodic averages and will shorten the burn-in period, or convergence to equilibrium, in most scenarios of interest. A simple approach to reduce variability, amenable to parallel computations, consists of averaging independent estimators. However, while averaging estimators of $π$ in a pseudo-marginal algorithm retains the guarantee of sampling from $π$ asymptotically, naive averaging of acceptance ratio estimates breaks detailed balance, leading to incorrect results. We propose an original methodology which allows for a correct implementation of this idea. We establish theoretical properties which parallel those available for standard PM algorithms and discussed above. We demonstrate the interest of the approach on various inference problems. In particular we show that convergence to equilibrium can be significantly shortened, therefore offering the possibility to reduce a user's waiting time in a generic fashion when a parallel computing architecture is available.

stat.CO↗

arXiv2016

MCMC Shape Sampling for Image Segmentation with Nonparametric Shape Priors

Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation algorithms optimize an energy functional and find a point estimate for the object to be segmented. This does not provide a measure of the degree of confidence in that result, neither does it provide a picture of other probable solutions based on the data and the priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior densities of the shapes of the objects to be segmented. For such characterization, we propose a Markov chain Monte Carlo (MCMC) sampling-based image segmentation algorithm that uses statistical shape priors. In addition to better characterization of the statistical structure of the problem, such an approach would also have the potential to address issues with getting stuck at local optima, suffered by existing shape-based segmentation methods. Our approach is able to characterize the posterior probability density in the space of shapes through its samples, and to return multiple solutions, potentially from different modes of a multimodal probability density, which would be encountered, e.g., in segmenting objects from multiple shape classes. We present promising results on a variety of data sets. We also provide an extension for segmenting shapes of objects with parts that can go through independent shape variations. This extension involves the use of local shape priors on object parts and provides robustness to limitations in shape training data size.

cs.CV↗

arXiv2016

On the Use of Penalty MCMC for Differential Privacy

We view the penalty algorithm of Ceperley and Dewing (1999), a Markov chain Monte Carlo (MCMC) algorithm for Bayesian inference, in the context of data privacy. Specifically, we study differential privacy of the penalty algorithm and advocate its use for data privacy. We show that in the simple model of independent observations the algorithm has desirable convergence and privacy properties that scale with data size. Two special cases are also investigated and privacy preserving schemes are proposed for those cases: (i) Data are distributed among several data owners who are interested in the inference of a common parameter while preserving their data privacy. (ii) The data likelihood belongs to an exponential family.

stat.CO↗

arXiv2014

Bayesian tracking and parameter learning for non-linear multiple target tracking models

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, which constitutes the solution to the tracking problem, as well as the model parameters. In the numerical section, we present performance comparisons with several competing techniques and demonstrate significant performance improvements in all cases.

stat.AP↗