Human computation or crowdsourcing involves joint inference of the ground-truth-answers and the worker-abilities by optimizing an objective function, for instance, by maximizing the data likelihood based on an assumed underlying model. A variety of methods have been proposed in the literature to address this inference …
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48 results for “Convex Inference”
Introduces VH bound for approximate Bayesian inference.
problem Approximate Bayesian inference with intractable integrals.
method Minimizes convex upper bound to intractable integral.
result VH bound leads to convex optimization problem.
Paper infers intrinsic dimension from quasi-convex measurements.
problem Inferring intrinsic dimension from measurements by quasi-convex functions.
method Developed a method using filtration of Dowker complexes based on discrete data of point orderings.
result Correct intrinsic dimension can be inferred in the limit of large data under generic assumptions.
Unified framework improves robust causal inference, overcoming Gaussian barriers and optimization issues.
problem Improving robust causal inference in non-Gaussian settings.
method Combines gamma-Divergence, GNC, and Gatekeeper mechanism.
result Enhanced robustness and global optimization in causal effect estimation.
New method improves MAP inference for CGMs on path graphs, avoiding approximation and maintaining integrality.
problem Improving MAP inference for aggregated count data in CGMs with small values.
method Formulated as a minimum cost flow problem, solved using DCA with efficient subroutines.
result Outputs higher quality solutions than conventional methods.
The paper tackles MAP inference over non-convex constraints in safety-critical settings.
problem Efficiently computing MAP predictions subject to non-convex constraints is challenging.
method The paper investigates conditions for exact and efficient MAP inference over continuous variables and devises scalable algorithms for both tractable and general cases.
result The proposed methods outperform constraint-agnostic baselines and scale to complex densities.
A new method for statistical inference using approximate Newton steps from stochastic gradients.
problem Efficient statistical inference for convex and non-convex learning problems.
method Approximate stochastic Newton steps based on finite differences.
result Efficient computation of statistical error covariance without exact second-order information.
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference process is first defined to be the minimization of a convex f…
The paper tackles partial inference in structured prediction using a convex optimization approach.
problem Maximizing a score function with unary and pairwise potentials in graph label spaces.
method Generative model approach with two-stage convex optimization for label recovery.
result Conditions for recovering a majority of labels with provable guarantees.
Paper tackles non-convex optimization and statistical inference for tensor graphical models.
problem Estimating and inferring dependency structure in tensor-valued data.
method Alternating minimization algorithm for non-convex optimization and de-biased statistical inference.
result Proves alternating minimization attains optimal statistical rate of convergence and proposes FDR control for testing hypotheses.
ASVI automates variational inference for complex models.
problem Efficient variational inference for complex probabilistic models.
method Automatic structured variational inference (ASVI) using convex updates.
result ASVI outperforms other methods on a wide range of problems.
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probab…
Novel technique reduces Bayesian network complexity while preserving inference accuracy.
problem Complexity reduction in Bayesian networks for efficient inference.
method Directed convex hull structure and polynomial-time algorithm for identifying minimum localized networks.
result High dimension reduction capability and improved inference efficiency in real networks.
Active-set algorithm improves Cox regression for shape-restricted covariates.
problem Improving Cox regression for shape-restricted covariates.
method Shape-restricted inference using active-set optimization for spline basis expansion.
result Active-set algorithm produces accurate linear covariate effect estimates.
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
We simplify inference for TPP models with latent structures.
problem Intractable marginalization in TPP models with latent structures.
method Approximate inference over latent variables using a tight upper bound on the approximation gap.
result Improved results for models like Survival Analysis.
A new method improves SVI for high-dimensional, poorly-conditioned distributions.
problem Challenges in existing SVI methods for high-dimensional, poorly-conditioned distributions.
method Trust-region optimization approach leveraging conditional independences and second-order information.
result Superior numerical performance and better scalability in high-dimensional distributions.
New method shows MMSE inference can be solved via convex optimization in high dimensions.
problem Optimal Bayesian MMSE inference in high dimensions is computationally hard.
method Minimizing convex loss and regularizer functions smoothed versions of MAP.
result Optimal MMSE performance achievable via M-estimation in high dimensions.
Paper estimates manifold reach using convexity defect function.
problem Estimating the reach of submanifolds from point clouds.
method Relates reach to convexity defect function, uses stability properties, and combines with recent estimators.
result Uniform expected loss bound and minimax rate lower bounds for reach estimation are provided.
New method for fast inference in diffusion models.
problem Intractable probabilistic inference in diffusion models.
method Variational Gaussian Process, exponential family description, convex optimization.
result Improved fast algorithm for learning model parameters.
AIF reformulated as convex MDP for adaptive behavior.
problem Adaptive behavior and policy optimization.
method Formulating AIF as convex MDP, deriving mirror descent algorithm.
result EFE minimization in AIF is equivalent to reward maximization in latent MDP, with epistemic component.
Online SGD achieves consistent estimation in high-dimensional non-convex inference tasks.
problem Consistent estimation in high-dimensional non-convex optimization problems.
method Online stochastic gradient descent (SGD) on non-convex losses.
result Nearly sharp thresholds for sample complexity in high-dimensional settings.
Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applicationsmath.OC
Estimates convex hulls of smooth function images with error bounds.
problem Estimating the convex hull of the image of a smooth boundary set.
method Using submersion properties and sampling inputs, derive bounds on Hausdorff distance.
result New tighter and more general error bounds for geometric inference.
Paper introduces new method for statistical inference with stochastic gradients.
problem Uncertainty quantification for solutions from iterative optimization methods.
method Moment-adjusted stochastic gradient descent.
result Established non-asymptotic theory for statistical inference.
Bayesian inference becomes tractable with log-concave priors and targets.
problem Transforming samples from a prior to a posterior distribution efficiently.
method Optimal transport theory and convex optimization.
result Log-concave priors and targets allow for efficient Bayesian inference.
Adaptive conformal inference without data exchangeability assumptions.
problem Real-world scenarios often violate the data exchangeability assumption for conformal prediction.
method Parameter-free online convex optimization for adaptive conformal inference.
result Controls long-term miscoverage frequency at a nominal level empirically.
The paper develops sum-of-squares relaxations for computing -divergences.
problem Computing -divergences from non-centered covariance matrices.
method Sum-of-squares relaxations for convex optimization.
result Sum-of-squares relaxations make computations tractable.
New method improves MAP inference efficiency and reliability.
problem Efficient inference in systems with latent variables or missing data.
method Generalized dual decomposition on a convex decomposition bound.
result Framework converges monotonically and is faster/reliable than previous methods.
Convex Optimization in Juliamath.OC
This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies …
Bayesian inference over admissible histories leads to irreversible kinetics.
problem Modeling irreversible processes in systems with uncertain histories.
method A Gibbs-type measure weighted by energy-dissipation action and observation constraints, interpreted as a Bayesian posterior.
result The measure concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution.
Paper characterizes gradient descent in high-dimensional learning problems.
problem Understanding gradient descent dynamics in high-dimensional statistical learning.
method Non-asymptotic joint distributional characterization of gradient descent iterates and debiased statistics.
result Gradient descent iterates approximate normality after debiasing correction.
Optimal neural network approximation for Wasserstein gradient direction via convex optimization.
problem Approximating Wasserstein gradient direction with limited data.
method Two-layer networks with squared-ReLU activations, SDP relaxation.
result Optimal approximation of Wasserstein gradient direction in two-layer networks.
Sharp bounds on binary model inference performance.
problem High-dimensional inference in binary models.
method Convex empirical risk minimization, sharp asymptotics, optimal performance bounds.
result Sharp predictions and optimal performance bounds for binary models.
This paper improves matrix completion by estimating uncertainty and performing inference.
problem Estimating a low-rank matrix with noisy and incomplete data and assessing uncertainty.
method Developed a de-biased estimator procedure to compensate for bias in convex and nonconvex estimators.
result Achieved nearly precise non-asymptotic distributional characterizations for de-biased estimators, enabling valid confidence intervals.
Geometric analysis improves convergence of variational inference.
problem Challenges in analyzing convergence of variational inference due to non-convexity and non-smoothness.
method Exploits exponential family structure and Bregman divergences to geometrically analyze the optimization landscape.
result Establishes non-asymptotic convergence rates for gradient descent algorithms.
One-dimensional crystals have convex shapes under certain conditions.
problem Determining if one-dimensional crystals have convex shapes.
method Analyzing the free energy under mass constraints and convexity assumptions.
result In one dimension, crystals have convex shapes under given conditions.
Convergent Message-Passing Algorithms for Inference over General Graphs with Convex Free Energiescs.LG
Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases o…
Proposes a differentiable LSE-ICNN for modeling multi-well potentials.
problem Modeling multi-well potentials in various scientific domains.
method Log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes.
result Smooth surrogate that retains convexity within basins and allows gradient-based learning.
Proves FR-NGD optimally approximates evolutionary dynamics and continuous Bayesian inference.
problem Optimizing continuous time replicator equations and continuous Bayesian inference.
method Fisher-Rao natural gradient descent (FR-NGD) and its correspondence with evolutionary dynamics.
result FR-NGD optimally approximates continuous time replicator equations and continuous Bayesian inference.
Paper develops methods for statistical inference with SGD in nonconvex optimization.
problem Statistical inference for nonconvex optimization problems.
method Proposes two online inferential procedures combining SGD and bootstrap techniques.
result Establishes error convergence rates and asymptotically valid bootstrap confidence intervals.
Adaptive approximations improve variational inference for complex models.
problem Efficiently approximate marginal distributions and partition functions in complex probabilistic models.
method Two classes of adaptive approximations that include Bethe, tree-reweighted, and convex free energies.
result Proposed approximations automatically adapt to a given model and outperform existing methods.
VIRTUAL improves federated multi-task learning for non-convex models.
problem Real-world federated datasets show statistical heterogeneity.
method VIRTUAL treats federated network as a star-shaped Bayesian network and uses variational inference.
result VIRTUAL outperforms state-of-the-art for federated learning on real-world datasets.
Convex polytope trees expand decision trees with interpretable boundaries.
problem High accuracy often requires many nodes in decision trees, reducing interpretability.
method CPT uses logical disjunction of weighted linear decision-makers, geometrically a convex polytope.
result CPT achieves high accuracy with fewer nodes compared to existing methods.
TRAiL is a linear bandit algorithm that ensures optimal regret and guarantees inference quality.
problem Optimal regret and inference quality in linear bandits with convex action sets.
method TRAiL estimates the parameter through regularized least squares and perturbs the action set along the tangent plane.
result TRAiL achieves an upper bound on cumulative regret with high probability.
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they str…
This paper proposes a method to automatically infer the quantile parameter in machine learning.
problem Estimating the quantile parameter in asymmetric loss functions.
method Jointly infers the quantile parameter and function parameters using convexity properties and a gradient boosting algorithm.
result The proposed method can automatically recover the quantile parameter and improve function parameter recovery.
Softplus regressions use multiple hyperplanes to classify data.
problem Classifying data with flexible nonlinear decision boundaries.
method Softplus function based regression models convolving gamma distributions.
result Softplus regressions achieve comparable classification accuracy to SVM but with less computation.
Stochastic annealing improves variational inference for Bayesian models.
problem Finding better local optimal solutions in variational inference.
method Empirical evaluation of stochastic annealing for Bayesian posterior optimization.
result Stochastic annealing provides clear improvement on GMM and HMM, while LDA favors deterministic annealing.