Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorit…
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23 results for “A-optimality”
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
We study the optimal design problems where the goal is to choose a set of linear measurements to obtain the most accurate estimate of an unknown vector in dimensions. We study the -optimal design variant where the objective is to minimize the average variance of the error in the maximum likelihood estimate of th…
Study on computable online learning with new conditions and complexities.
problem Characterizing optimal online learning under varying optimality requirements.
method Introduced anytime optimal (a-optimal) online learning and explored computational separations.
result Found a computational separation between a-optimal and optimal online learning.
Scalable method for Bayesian experimental design without integrating over posterior distributionmath.NA
Efficiently designs experiments without integrating posterior distributions.
problem Computational inefficiency in Bayesian experimental design for PDE-based models.
method Likelihood-free approach using ANN to approximate conditional expectation.
result Significant reduction in observation model evaluations.
In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the corresponding responses will lead to a good estimator of the model. A classical approach …
Optimal Sampling for Generalized Linear Model under Measurement Constraint with Surrogate Variablesstat.ME
Optimal sampling strategy improves prediction accuracy with surrogate variables under measurement constraints.
problem Measurement-constrained datasets and lack of labeled data.
method A-optimality criterion for optimal sampling, leveraging surrogate variables.
result Achieves lower asymptotic variance and reduced empirical mean squared error.
We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate of the hidden parameter of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that…
-Regularized A-Optimal Design and its Approximation by -Regularized Proportional Volume Samplingcs.DS
This work introduces a new sampling method to approximate an optimal design problem in ridge regression.
problem Finding an optimal subset of predictors in ridge regression to minimize prediction error.
method Developed a -regularized proportional volume sampling algorithm with approximation guarantees.
result The algorithm provides a -approximation for the optimal design problem.
We provide an overview of several non-linear activation functions in a neural network architecture that have proven successful in many machine learning applications. We conduct an empirical analysis on the effectiveness of using these function on the MNIST classification task, with the aim of clarifying which functions…
AMP algorithms can be efficiently simulated by SDPs even with corrupted data.
problem Optimizing average-case optimization problems with corrupted data.
method Local statistics hierarchy semidefinite programs (SDPs) simulate AMP algorithms robustly.
result Robust guarantees for many AMP algorithms are offered, contrasting with strong lower bounds for SDPs.
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI proble…
A new method for automatically aligning and clustering time series data.
problem Challenges in aligning and clustering time series data, especially without a template signal.
method TROUT (Temporal Registration using Optimal Unitary Transformations) method based on a novel dissimilarity measure.
result TROUT outperforms competitors in clustering time series data.
Adaptive algorithm reduces regret in causal bandits.
problem Minimize regret in causal bandits with unknown d-separators.
method Adaptive algorithm exploiting d-separators without prior knowledge.
result Significantly smaller regret than previous methods.
Unpaired deep learning reconstructs MRI images from accelerated data.
problem Difficulty in acquiring matched fully sampled k-space data for supervised deep learning.
method Optimal transport driven cycleGAN architecture.
result Reconstructs high resolution MR images from accelerated k-space data.
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
problem Developing a more accurate discrete Laplacian for 3D meshes.
method Proves the Euler-Lagrange equation for the Dirichlet energy using the associated discrete Laplacian of the dual construction.
result The associated discrete Laplacian is optimal in compared to the primal construction.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
The paper solves a maximum entropy sampling problem with efficient algorithms and performance guarantees.
problem Selecting the most informative principal submatrix from a covariance matrix.
method Derive a novel convex integer program, develop efficient sampling algorithms with approximation bounds, and analyze local search algorithms.
result Efficient algorithms with near-optimal performance guarantees for solving MESP and A-MESP.
Bayesian framework improves variance component estimation in MET data.
problem Inaccurate estimation of variance components in MET data.
method Proposes a Bayesian updating framework using historical data.
result Stabilizes variance component estimation and quantifies uncertainty.
The operator over an almost complex manifold induces canonical connections of type over the bundles of -forms. If the almost complex structure is integrable then the previous connections induce the canonical holomorphic structures of the bundles of -forms. For we can …
New findings show that common optimization algorithms struggle with random problems.
problem Finding near-optimal solutions to random optimization problems.
method Low-degree polynomials, Boolean circuits, and Langevin dynamics.
result These algorithms fail to produce nearly optimal solutions with high probability.
Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flowscs.LG
Develops c-GNF for personalized social science policy analysis.
problem Challenges in estimating causal effects and counterfactual inference in social sciences.
method causal-Graphical Normalizing Flow (c-GNF) method.
result c-GNF performs well in estimating causal effects and counterfactual inference.
New algorithm reduces offline RL sample complexity for MDPs.
problem Learning optimal policies from offline data in unknown MDPs.
method Adaptive Pessimistic Value Iteration (APVI) algorithm.
result Suboptimality bound nearly matches theoretical limits.