Estimates chirp signal frequencies using probabilistic models.
problem Estimating instantaneous frequencies of chirp signals when true forms are unknown.
method Non-linear Gaussian processes and stochastic filters/smothers for posterior estimation.
result The method outperforms state-of-the-art methods on synthetic and real-world datasets.
Novel method uses Bayesian filters and PCRLB for state estimation of option prices.
problem Estimating unobserved latent variables from option prices.
method Posterior Cramer-Rao Lower Bound (PCRLB) based adaptive state estimation using various Bayesian filters.
result Proposed method outperforms individual filters and improves forecasting.
Study on conditions for achieving optimal robustness in statistical estimators.
problem Achieving the optimal robustness of estimators in statistical models.
method Developed a Wasserstein analogue of the Cramer-Rao inequality and investigated conditions for achieving the Wasserstein-Cramer-Rao lower bound.
result Conditions for the existence of asymptotically efficient estimators in one-parameter models and location-scale families.
Proposes a learned Bayesian Cramér-Rao bound for unknown measurement models.
problem Computing the Bayesian Cramér-Rao bound requires full knowledge of priors and measurement distributions.
method Introduces a Physics-encoded score neural network to learn priors and measurements.
result Demonstrates improved sample complexity and interpretability through domain knowledge incorporation.
The paper generalizes Bayesian Cramér-Rao inequality using information geometry of relative α-entropy.
problem Establishing a lower bound for the variance of an unbiased estimator for the α-escort distribution.
method Proposes a general Riemannian metric based on relative α-entropy to derive a generalized Bayesian Cramér-Rao inequality.
result Establishes a lower bound for the variance of an unbiased estimator for the α-escort distribution.
New theory of sensitivity for unbiased estimators using Wasserstein geometry.
problem Estimating the instability of estimators under small perturbations.
method Developed a new theory based on Wasserstein geometry, analogous to classical Cramér-Rao theory.
result Wasserstein-Cramér-Rao lower bound for sensitivity of unbiased estimators.
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
This work uses Sylvester normalizing flows for more accurate metabolite quantification in MRS.
problem Challenges in accurate metabolite quantification in MRS due to spectral overlap, low SNR, and artifacts.
method Bayesian inference framework with physics-informed Sylvester normalizing flows.
result Accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models …
Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
problem Improving estimator efficiency in non-asymptotic settings.
method Incorporates curvature-aware corrections based on extrinsic geometry of statistical model manifold.
result Meaningful tightening of estimator variance bounds.
We study the geometry of probability distributions with respect to a generalized family of Csiszár f-divergences. A member of this family is the relative α-entropy which is also a Rényi analog of relative entropy in information theory and known as logarithmic or projective power divergence in statistics. We apply E…
This work introduces a new data-driven estimator for the Bayesian Cramér-Rao bound using score matching.
problem Benchmarking the performance of statistical estimators and providing a principled metric for system design and optimization.
method Score matching technique to estimate the Bayesian Cramér-Rao bound from training data.
result Developed novel non-asymptotic bounds on the score matching error and the Bayesian CRB estimator.
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve O(n−1/2) convergence rate under regularity assumptions. Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
We consider the problem of off-policy evaluation for reinforcement learning, where the goal is to estimate the expected reward of a target policy π using offline data collected by running a logging policy μ. Standard importance-sampling based approaches for this problem suffer from a variance that scales exponentia…
Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.
problem Efficient tensor decomposition for count data models.
method Rank-constrained maximum-likelihood estimator for tensor decomposition.
result Achieves multiway analysis with variance matching Cramér-Rao Lower Bound up to constants and logarithmic factors.
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n and arbitrary f. Paper extends Bayesian Cramér-Rao bound with geometric considerations.
problem Estimation of covariance matrices with geometric structures.
method Intrinsic Bayesian Cramér-Rao bound with Riemannian geometry.
result Performance bounds for covariance matrix estimation.
In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the Chi-square divergence and the expectation value of the estimator. By using the relation b…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermi…
Donald Trump was lagging behind in nearly all opinion polls leading up to the 2016 US presidential election, but he surprisingly won the election. This raises the following important questions: 1) why most opinion polls were not accurate in 2016? and 2) how to improve the accuracies of opinion polls? In this paper, we …
A new method for state estimation in state-space models using incomplete data.
problem State estimation in nonlinear state-space models with incomplete observations.
method Statistical analysis of incomplete observations, score function, observed information matrices, EM-gradient-particle filtering.
result Maximum likelihood estimation of state-vector with explicit form of observed information matrix.
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
The report studies ranking from pairwise comparisons in graphs, achieving optimal error bounds and proposing efficient algorithms.
problem Ranking items from pairwise comparisons in general graphs and graphs with locality.
method Maximum likelihood estimation (MLE) and preconditioned gradient descent for general graphs; divide-and-conquer algorithms for graphs with locality.
result MLE achieves optimal error bounds in general graphs and identifies conditions for locality.
Paper provides a new lower bound on MMSE using Poincaré inequality.
problem Estimating X from noisy Y in exponential family noise.
method Alternative MMSE representation + Poincaré inequality.
result New lower bound on MMSE holds for all distributions.
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
problem Estimation theory for finite-dimensional C*-algebras.
method Geometrical formulation of estimation theory.
result Derivation of Cramer-Rao and Helstrom bounds.
Guaranteed bounds for posterior inference in probabilistic programs.
problem Approximating the posterior distribution of probabilistic programs with provable correctness.
method Interval-based trace semantics, soundness and completeness proofs, weight-aware interval type system.
result Guaranteed bounds on the posterior distribution of probabilistic programs are computed and proven to be correct.
This paper studies the problem of inferring a global preference based on the partial rankings provided by many users over different subsets of items according to the Plackett-Luce model. A question of particular interest is how to optimally assign items to users for ranking and how many item assignments are needed to a…
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.
problem Estimating Laplacian matrices with structural constraints and sparsity.
method Linear reparametrization and closed-form expressions for Cramer-Rao bounds tailored to Laplacian matrix estimation.
result The derived CRBs provide performance limits for Laplacian matrix estimation and are validated in various applications.
Paper introduces geometry-aware normalizing flows for improved causal inference.
problem Disparity between sample and population distributions in causal inference.
method Integrates continuous normalizing flows with parametric submodels, employing Wasserstein gradient flows and optimal transport.
result Significantly reduces parameter estimation bias and variance in finite-sample settings.
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the stat…
Paper develops a new estimator for MDPs' risk functionals with lower variance and bias.
problem Estimating the distribution of returns in MDPs with high variance and bias.
method Developed a doubly robust (DR) estimator for the CDF of returns in MDPs, incorporating model-based estimation to mitigate variance issues.
result The DR estimator achieves lower variance and bias compared to IS estimators, and matches minimax lower bounds.
New CRB derived for curved models using extrinsic geometry.
problem Estimate curved statistical families accurately.
method Vector generalization of CRB with curvature correction using SDP and SOS relaxations.
result Directional curvature correction provides more accurate estimation.
A new algorithm optimizes Gaussian process posterior mean functions efficiently.
problem Optimizing Gaussian process posterior mean functions over hyperrectangles is challenging due to nonlinearity and nonconvexity.
method PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound.
result PALM-Mean improves scalability for large datasets compared to general-purpose solvers.
BayesBag improves reproducibility of Bayesian inference under model misspecification.
problem Bayesian posteriors can be unreliable and inconsistent under model misspecification.
method Apply bagging to the Bayesian posterior to improve reproducibility.
result Bagged posteriors typically satisfy reproducibility criteria under misspecification.
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild dif…
Improves GP models with known bounds for sampling and optimization.
problem Functions with known upper and lower bounds.
method Transforms GP models with bounds for posterior sampling and BO.
result Bounded entropy search (BES) selects points satisfying constraints.
The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.
problem Understanding the limits of adaptive LQR with unknown B-matrix.
method Local asymptotic minimax regret lower bounds using van Trees' inequality and Bellman error representation.
result Logarithmic regret is impossible if the parametrization induces an uninformative optimal policy.
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using …
Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the ident…
The Fisher-Rao geometry is applied to elliptical distributions for optimization and classification.
problem Optimizing and classifying covariance matrices using geometric tools.
method Riemannian optimization and intrinsic Cramér-Rao bounds.
result Geometric tools enhance covariance matrix estimation and classification.
Adaptive Heston model calibration using PCRLB and switching filters.
problem Estimating volatility in stochastic volatility models like Heston.
method Bayesian filtering (EKF, UKF, PF) with PCRLB for parameter estimation.
result Adaptive estimation of Heston model parameters improves volatility estimation.
In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during training. Variational Autoencoders (VAE) are one important example where variation…
This work improves bounds on Bayesian coreset quality.
problem Limitations of existing theoretical analysis of Bayesian coresets.
method Develops general upper and lower bounds on KL divergence.
result Demonstrates flexibility of new theoretical bounds in various models.
We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provid…
Variational Auto-encoders (VAEs) have been very successful as methods for forming compressed latent representations of complex, often high-dimensional, data. In this paper, we derive an alternative variational lower bound from the one common in VAEs, which aims to minimize aggregate information loss. Using our lower bo…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is…