Gradient-Based Variational Inference (GradVI) for Empirical Bayes Multiple Regression with Application to Trend Filtering
This paper introduces GradVI, a gradient-based optimization method for variational empirical Bayes (VEB) in multiple linear regression, demonstrating its advantages over coordinate ascent methods (CAVI) in scenarios with correlated predictors or design matrices enabling fast matrix-vector multiplication, particularly in trend filtering applications.
Functional Normalizing Flow: A Discretization-Invariant Variational Inference Method for Solving Inverse Problems of Partial Differential Equations
This paper introduces functional normalizing flow, a novel discretization-invariant variational inference method for efficiently solving inverse problems of partial differential equations in infinite-dimensional space.
수정된 변분 추정기를 사용한 포아송 로그 정규 모델에서의 매개변수 불확실성 평가
본 논문에서는 샌드위치 추정기를 사용하여 포아송 로그 정규 모델에서 변분 추정기의 일관성과 점근적 정규성을 조사하고, 변분 추정기의 분산을 추정하기 위해 샌드위치 추정기가 변분적 피셔 정보 방법보다 효과적임을 보여줍니다.
修正変分推定を用いたポアソン対数正規モデルにおけるパラメータの不確実性の評価
本稿では、カウントデータ分析で広く用いられるポアソン対数正規モデル(PLN)のパラメータ推定において、従来の変分推定法では困難であった信頼区間の構築を実現する、サンドイッチ推定に基づく分散推定手法を提案し、その有効性をシミュレーションと実データ分析を通じて検証しています。
Evaluating Parameter Uncertainty in the Poisson Lognormal Model Using Corrected Variational Estimators: A Comparison with Variational Fisher Information
This research paper proposes and evaluates the Sandwich estimator, derived from M-estimation theory, as a more accurate alternative to the Variational Fisher Information method for estimating the variance of parameters in the Poisson Lognormal (PLN) model, particularly for high-dimensional data.
Variational Inference for Pairwise Markov Random Fields on the Boolean Hypercube Using Quantum Entropy
This research paper introduces a novel approach to variational inference for pairwise Markov Random Fields on the Boolean hypercube, leveraging quantum relaxations of the Kullback-Leibler divergence to derive tractable upper bounds on the log-partition function.
EigenVI: A Novel Approach to Black-Box Variational Inference Using Score Matching and Orthogonal Function Expansions
EigenVI is a new algorithm for black-box variational inference that leverages orthogonal function expansions to construct flexible variational approximations and utilizes score matching to derive a computationally efficient optimization procedure based on solving a minimum eigenvalue problem.
Patched Batch-and-Match: Scaling Score-Based Variational Inference to High Dimensions with Low-Rank Approximations
The paper introduces a new algorithm, patched batch-and-match (pBaM), for scaling score-based variational inference to high-dimensional problems by efficiently approximating full covariance matrices with a combination of low-rank and diagonal structures.
Wasserstein Gradient Flow for Variational Inference with Mixture Models: A Particle-Based Approach
This paper proposes a novel approach to variational inference (VI) that leverages Wasserstein gradient flows (WGFs) over the space of variational parameters, offering a unified perspective on existing methods and enabling efficient approximation of complex posterior distributions, particularly with mixture models.
Minimizing Regularized R'enyi Divergence Using Bregman Proximal Gradient Algorithms: A Novel Approach to Variational Inference
This paper introduces a novel variational inference algorithm based on Bregman proximal gradient descent that minimizes the regularized R'enyi divergence between a target distribution and an approximating distribution from an exponential family, offering theoretical convergence guarantees and practical advantages over existing methods.
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