Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
A similarity label indicates whether two instances belong to the same class while a class label shows the class of the instance. Without class labels, a multi-class classifier could be learned from similarity-labeled pairwise data by meta classification learning. However, since the similarity label is less informative …
Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive poste…
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
Logistic regression can handle noisy labels effectively when labels are imperfectly assigned by multiple experts.
problem Label noise in supervised classification due to manual labelling by multiple experts.
method Using approximate posterior probabilities of class membership from multiple experts to train logistic regression models.
result Logistic regression can be robust to label noise when classification difficulty is the only source of errors.
We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables proje…
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
Efficiently infers coupled hidden Markov models with noisy discrete observations.
problem Intractable inference for coupled continuous-time Markov chains with discrete observations.
method Latent Interacting Particle Systems, look-ahead functions, twisted Sequential Monte Carlo sampling.
result Demonstrated effectiveness on latent SIRS model and wildfire spread dynamics.
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
problem Learning elliptic PDEs with noisy data and non-homogeneous boundary conditions.
method Bayesian approach with a Hölder space prior on neural network weights.
result Posterior contracts at near-minimax rate without prior knowledge of solution smoothness.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Bayesian PINNs solve noisy PDE problems with physics constraints.
problem Uncertainty quantification in noisy PDE problems.
method Bayesian framework combining PINNs and HMC/VI for posterior estimation.
result HMC outperforms VI for noisy data.
Bayesian approach optimizes quantum circuits for noisy hardware.
problem Optimizing parameterized quantum circuits on noisy quantum hardware.
method Reformulate classical optimisation as Bayesian posterior, combining cost function and prior distribution. Apply dimension reduction and posterior sampling strategies.
result Bayesian approach generates faster, less noisy circuits than classical methods.
Noise-ignorant empirical risk minimization achieves state-of-the-art performance on noisy data.
problem Learning with noisy labels in multi-class classification problems.
method Introducing relative signal strength (RSS) to quantify transferability and applying Noise Ignorant Empirical Risk Minimization (NI-ERM).
result NI-ERM achieves state-of-the-art performance on CIFAR-N data challenge.
New method learns multi-class from single-class data with confidences.
problem Learning multi-class from single-class data without additional data.
method Empirical risk minimization framework for multi-class classification.
result Method achieves Bayes-consistency with noisy confidences.
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despi…
VBMC+VIQR outperforms noisy models in Bayesian inference.
problem Bayesian inference with noisy likelihoods in complex models.
method Gaussian process surrogates, expected information gain, variational interquantile range.
result VBMC+VIQR achieves state-of-the-art performance in noisy inference benchmarks.
Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without leveraging the structures of the generative models. In this paper, we propose Amorti…
The paper improves model robustness by regularizing posterior differences.
problem Improving model robustness in noisy input scenarios.
method Posterior differential regularization with f-divergence. result Regularizing with f-divergence improves model robustness. Develops NPMC method for noisy labels, improving multiclass classification accuracy.
problem Asymmetric misclassification costs and label noise in multiclass classification.
method Empirical likelihood approach using exponential tilting density ratio model.
result Root n consistent and asymptotically normal estimators for clean labels and noise mechanism.
We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contribu…
Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive w…
A new particle filter uses diffusion models to improve state estimation from noisy data.
problem Sequentially estimating the state of a dynamical system from noisy and incomplete observations.
method Uses a diffusion model to simulate and predict system dynamics, incorporating noisy observations to refine predicted states.
result An unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.
In label-noise learning, \textit{noise transition matrix}, denoting the probabilities that clean labels flip into noisy labels, plays a central role in building \textit{statistically consistent classifiers}. Existing theories have shown that the transition matrix can be learned by exploiting \textit{anchor points} (i.e…
Bayesian approach learns linear operators from noisy data.
problem Learning linear operators from noisy data in infinite-dimensional spaces.
method Bayesian approach with Gaussian priors.
result Establishes posterior contraction rates and generalization error guarantees.
Method learns dynamics from noisy partial observations.
problem Reconstructing stochastic dynamical systems from indirect noisy data.
method Amortized path generation method for nonlinear stochastic filtering.
result Learned conditional path generator quantifies uncertainty.
Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in human-machine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and nonstationary nature. Current methodologies for analyzing these signals often fall short bec…
The scalability of the labeling process and the attainable quality of labels have become limiting factors for many applications of machine learning. The programmatic creation of labeled datasets via the synthesis of noisy heuristics provides a promising avenue to address this problem. We propose to improve modeling of …
Simulation-free VI closes the approximation gap in latent SDEs
problem Recovering dynamical systems from noisy observations
method Helmholtz-SDE
result Recovers dynamics more faithfully than prior methods
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the conditional mean of the labels and accounting for the linearisation error. PL has s…
We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data …
Attention-only transformers learn from context via two stages of inference.
problem Learning from corrupted token sequences in minimal transformers.
method Two-stage empirical Bayes interpretation: kernel-weighted posterior mean and particle dynamics.
result Effective denoising without explicit noise schedules, showing posterior-mean recovery under asymptotic conditions.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
We solve a complex Bayesian control problem with novel methods.
problem Optimizing control of a hidden signal's influence on noisy observations.
method Measure-valued HJB perspective, viscosity theory, approximation arguments.
result Equivalence to HJB equation and continuous viscosity solution.
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of…
VSE estimates complex processes from noisy measurements without a model.
problem Estimating states of complex, model-free processes from noisy data.
method Variational state estimation using recurrent neural networks (RNNs) in both learning and inference phases.
result VSE provides a competitive state estimate for a benchmark process (Lorenz system) compared to known and data-driven methods.
Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering in the data, where it is assumed that meaningful correlation structure exists ac…
FSGLD improves federated data sampling by correcting noisy gradients.
problem Noisy gradients and delayed communication in federated data.
method Conductive gradients to correct noisy gradients in distributed SGLD.
result FSGLD converges to true posterior even with delayed communication.
Diffusion models help in learning priors for Thompson Sampling in bandit problems.
problem Learning effective strategies for diverse bandit tasks.
method Training a denoising diffusion model to learn task distributions, combining with Thompson Sampling.
result The approach significantly improves performance across different bandit tasks.
SIP framework discovers governing equations in uncertain systems.
problem Discovering governing equations in systems with input variability and noisy data.
method SIP framework treats unknown coefficients as random variables and infers their posterior distribution by minimizing Kullback-Leibler divergence.
result SIP consistently identifies correct equations and lowers coefficient error by 82% relative to SINDy.
This paper treats prediction markets as Bayesian inverse problems to quantify uncertainty and identify event outcomes.
problem Uncertainty and identifiability in prediction market outcomes from price-volume histories.
method Formulates prediction markets as Bayesian inverse problems, introduces a log-odds observation model, and derives posterior uncertainty quantification and identifiability criteria.
result Explicit diagnostics for informative and stable inference regimes, and validation through synthetic data experiments.
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding th…
Paper analyzes GP-EI for Bayesian optimization with no regret and provides guidance on choosing incumbents.
problem Analyzing cumulative regret of GP-EI with different incumbents in noisy Bayesian optimization.
method Analyzes GP-EI with three incumbents (BPMI, BSPMI, BOI) in both SE and Matérn kernels, proving no-regret for BPMI and BSPMI.
result GP-EI with BPMI and BSPMI is a no-regret algorithm for both SE and Matérn kernels, providing theoretical guidance for choosing incumbents.
Variational inference provides approximations to the computationally intractable posterior distribution in Bayesian networks. A prominent medical application of noisy-or Bayesian network is to infer potential diseases given observed symptoms. Previous studies focus on approximating a handful of complicated pathological…
Improves state space models' resistance to noise.
problem State space models' initialization assumes noise-free data, which is often violated.
method Uncertainty-aware initialization for state space models, reformulating HiPPO with measurement noise.
result Improves model resistance to noise at training and inference time.
Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.
problem Sampling from noisy posterior distributions efficiently.
method Annealed Langevin dynamics combined with diffusion models.
result Achieves posterior sampling in polynomial time with a weaker score error bound.
DiEM trains diffusion models from noisy data using EM.
problem Training diffusion models requires clean data, which is often unavailable.
method DiEM uses expectation-maximization algorithm to train diffusion models from incomplete and noisy observations.
result DiEM leads to proper diffusion models suitable for downstream tasks.