PRCD-MAP learns to trust imperfect priors in causal discovery, improving accuracy and robustness.
problem Tackles the brittle trade-off between blind trust and rejection of external priors in causal discovery.
method Proposes PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to imperfect priors and modulates regularization in a MAP objective.
result Enjoys a population-level safety guarantee and outperforms existing methods on real-world causal discovery tasks.
New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
A new method maps high-dimensional Bayesian inverse problems to lower dimensions.
problem High-dimensional Bayesian inverse problems with complex prior information.
method Data-driven VAE prior and KRnet map for posterior approximation in latent space.
result Efficiently reduces computational cost and approximates posterior distributions.
Deep learning and prior maps improve traffic light recognition for autonomous cars.
problem Recognizing traffic lights for autonomous cars in urban environments.
method Combining deep learning-based detection with prior maps for traffic light identification and state recognition.
result The proposed system correctly identified relevant traffic lights along predefined routes.
This paper learns prior models from indirect data efficiently.
problem Learning prior models from indirect data in Bayesian inversion.
method Generative model of prior as pushforward of Gaussian in latent space, learned by minimizing loss function.
result Efficient residual-based neural operator approximation for forward model learning.
Solves imaging inverse problems using a VAE prior and joint MAP optimization.
problem Solving ill-posed inverse problems in imaging.
method Joint Posterior Maximization with a VAE prior, using alternate optimization algorithms and stochastic encoding.
result Converges to high-quality solutions close to bi-convex, outperforming non-convex MAP approaches.
Study characterizes training and test risks for MAP regression with Gaussian priors.
problem Understanding high-dimensional behavior of regularized linear regression with informative priors.
method Maximum a posteriori (MAP) regression with Gaussian priors, using random matrix theory.
result Closed-form risk formulas reveal the bias-variance-prior tradeoff and explain double descent.
Bayesian HMM for protein alignment state estimation.
problem Estimating the MAP state sequence for a Bayesian HMM.
method Training data with Dirichlet priors, iterative algorithms for MAP path estimation.
result Bayesian setup outperforms frequentist estimation in protein alignment.
Solves imaging inverse problems using autoencoding priors.
problem Ill-posed inverse problems in imaging.
method Joint Posterior Maximization with Autoencoding Prior (JPMAP).
result JPMAP converges to a stationary point and provides robust solutions.
New method learns disentangled representations using Gromov-Monge maps.
problem Learning disentangled representations from unlabelled data.
method Introduces a novel approach based on Gromov-Monge maps to preserve geometric features while aligning data distributions.
result Demonstrates effectiveness on four benchmarks, outperforming other methods.
Study connects Gaussian processes and regularization for sequence-function mappings.
problem Understanding and interpreting sequence-function maps in biology.
method Relates Gaussian process priors, regularization, and gauge fixing in overparameterized weight space.
result Established the relationship between regularized regression and Gaussian processes in function space.
Proposes a method to improve weakly supervised image segmentation using deep geodesic priors.
problem Limited availability of high-quality annotations for image segmentation, especially in medical data.
method Integrates a deep geodesic prior extracted from an auto-encoder to reduce the adverse effects of weak labels in segmentation accuracy.
result The proposed method significantly improves segmentation accuracy, boosting performance by 4.4% in dice score for clean labels and up to 6.3% for noisy labels (L2).
Estimates optimal transport maps with known cost functions.
problem Ensuring optimal transport maps correspond to real-world usefulness.
method Differentiable neural ground costs with known Monge map forms.
result General approach for incorporating prior information.
Study MAP estimation for PnP priors with SGD, proving convergence and demonstrating practical applications.
problem Theoretical analysis and practical implementation of PnP priors for Bayesian imaging problems.
method Maximum-a-posteriori estimation with Plug & Play priors and stochastic gradient descent.
result Convergence proof for MAP computation by PnP-SGD under realistic assumptions on the denoiser.
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. …
New algorithm proves convergence for MAP estimation with denoisers.
problem Proving convergence of MAP estimation methods using pretrained denoisers.
method A simple gradient descent algorithm on smoothed proximal objectives.
result Algorithm provably converges to the proximal operator under log-concavity.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. Generative autoencoders are those which are trained to softly enforce a prior on the latent distribution learned by the inference model. We call the distribution to …
Fast Bayesian inference with adaptable priors for real-time applications.
problem Intractable exact posterior computation limits Bayesian inference's adoption.
method Distribution Transformer architecture that learns mappings between priors and posteriors.
result Significant reduction in computation time from minutes to milliseconds.
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such …
Dropout regularization of deep neural networks has been a mysterious yet effective tool to prevent overfitting. Explanations for its success range from the prevention of "co-adapted" weights to it being a form of cheap Bayesian inference. We propose a novel framework for understanding multiplicative noise in neural net…
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…
This work improves the accuracy of OEF and DBV maps from qBOLD MRI data.
problem Noisy and inaccurate inference of OEF and DBV from qBOLD MRI data.
method Flexible amortized variational inference using a scaled multivariate logit-Normal distribution.
result Smooth and physiologically plausible OEF and DBV maps inferred with fewer training data.
JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.
problem Enforcing structure on derivatives of neural network mappings.
method Proposes using a neural network to directly learn the Jacobian of the input-output function, allowing control over derivative structure.
result Demonstrates learning invertible approximations to simple and 1-Lipschitz functions.
Generative models such as Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) are typically trained for a fixed prior distribution in the latent space, such as uniform or Gaussian. After a trained model is obtained, one can sample the Generator in various forms for exploration and understanding,…
New method needed for class prior estimation when covariates are reduced.
problem Class prior estimation fails under covariate shift when covariates are reduced.
method Propose a probing algorithm for class prior estimation.
result Provable transformations preserving covariate shift are necessary for class prior estimation.
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropri…
Statsformer validates and adapts LLM-derived semantic priors for improved supervised learning.
problem Unreliable semantic priors from LLMs can degrade supervised learning performance.
method Adapts LLM-derived feature scores into a family of learner-specific prior-injection mechanisms, calibrating their influence using out-of-fold validation.
result Improves prediction performance by adaptively downweighting unreliable LLM priors, ensuring a guardrailed statistical learning system.
New examples show some convex-cocompact subgroups are separable.
problem Whether all convex-cocompact subgroups are separable.
method Using Manning-Mj-Sageev construction, examples of separable subgroups of arbitrary finite rank are given.
result Examples of separable convex-cocompact subgroups of arbitrary finite rank exist.
Integrates inductive biases into VAEs using intermediary latent variables.
problem Ineffective mechanisms for incorporating inductive biases into VAEs.
method InteL-VAEs use an intermediary latent space to control encoding, with a parametric function to enforce desired properties.
result InteL-VAEs lead to better generative models and representations.
Enhances neural networks with prior function values to improve accuracy.
problem Improving neural network accuracy in regions without training data.
method Develops a probabilistic approach to augment BNNs with prior function values.
result Predictions rely more on prior information in uncertain regions.
Develops algorithms for Bayesian inference with Plug & Play priors, ensuring convergence and well-posedness.
problem Bayesian imaging inverse problems with implicit priors defined by denoising algorithms.
method Introduces PnP-ULA and PnP-SGD algorithms for Monte Carlo sampling and MAP inference, proving convergence under realistic assumptions.
result Proves convergence of PnP-ULA and PnP-SGD algorithms for Bayesian inference with PnP priors, targeting a well-posed decision-theoretic model.
A new model trains prior and encoder/decoder networks simultaneously for efficient generation.
problem Complex autoregressive prior in VQ-VAE models leads to slow generation.
method Builds a diffusion bridge between continuous and non-informative prior distributions.
result Model is competitive and efficient in optimization and sampling.
Combines diffusion maps and VAEs for scalable generative models.
problem Choosing a suitable prior for VAEs and GANs to match data topology.
method Variational Diffusion Autoencoders with Random Walk Sampling.
result Proves approximation theoretic results for dimension dependence.
Algorithm adapts to non-stationary rewards without prior knowledge.
problem Optimizing decisions in non-stationary environments without prior knowledge of changes.
method Optimization-based algorithm that restarts when non-stationarity is detected.
result Achieves tighter dynamic regret bound and is nearly minimax optimal.
AR-Flow VAE improves blind source separation with flexible autoregressive priors.
problem Unsupervised blind source separation of latent signals from mixtures.
method AR-Flow VAE uses autoregressive flows to model latent sources, enhancing flexibility and capturing complex dependencies.
result AR-Flow VAE effectively separates latent sources, demonstrating improved performance over conventional methods.
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework,…
We show that immersed minimal surfaces of R3 with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map is injective the whole surface is a wide component. Prior to these results it wa…
SAHMM-VAE separates sources adaptively using hidden Markov priors.
problem Unsupervised blind source separation.
method Source-wise adaptive Hidden Markov prior variational autoencoder.
result Different latent dimensions align with different source-specific temporal organizations.
Framework adapts to new tasks based on prior knowledge.
problem Models struggle to adapt to novel tasks without direct experience.
method Learned task representations and meta-mappings to transform them.
result Meta-mapping achieves 80-90% performance on novel tasks.
The paper characterizes mapping class groups related to abelian differentials.
problem Understanding the relationship between strata of abelian differentials and mapping class groups.
method Using the topological monodromy representation, the authors show that the fundamental group of a stratum surjects onto a specific subgroup of the mapping class group.
result The framed mapping class groups are finitely generated and explicitly characterized.
We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we argue that it might be advantageous to use more flexible code distributions. We de…
Develops methods for structured variational inference with star-structured models.
problem Inference in models with interdependent variables.
method Star-structured variational inference, existence, uniqueness, self-consistency proofs, approximation error bounds, gradient-based algorithm.
result First results for existence, uniqueness, and self-consistency of variational approximations in star-structured models.
A new method learns discrete representations for images and videos, improving upon previous models.
problem Learning discrete representations for images and videos to improve performance.
method Depthwise application of Vector Quantized Variational Autoencoders (VQVAE) to feature axis.
result 33% improvement in performance compared to previous discrete models.
Two applications of algebraic geometry improve surface mapping group actions.
problem Improving understanding of mapping class group actions on surface homology.
method Algebraic geometry techniques applied to Putman-Wieland conjecture.
result Non-unitary image of virtual action on H1(Σg′). Unified methodology for estimating optimal transport maps in various function spaces.
problem Estimating the function T given samples from P and T♯P. method Unified methodology based on Poincaré inequality and smooth convex function gradient.
result Nearly sharp results in various settings, including normal distribution and neural networks.