Regularization methods, specifically those which directly alter weights like and , are an integral part of many learning algorithms. Both the regularizers mentioned above are formulated by assuming certain priors in the parameter space and these assumptions, in some cases, induce sparsity in the parameter sp…
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48 results for “prior regularization”
Benefiting Deep Latent Variable Models via Learning the Prior and Removing Latent Regularizationcs.LG
New findings suggest latent regularization is unnecessary for high-quality image generation.
problem Improving image generation quality without latent regularization.
method Investigated the effect of latent regularization on image generation using learned priors.
result In the case of a sufficiently expressive prior, latent regularization is not necessary and may harm image quality.
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.
A simple regularization method improves model generalization.
problem Overfitting due to lack of labeled data in machine learning models.
method Density-fixing regularization method based on class prior distribution.
result Improves model generalization performance by approximating class prior distribution.
FlexAE addresses bias-variance trade-off in RAEs by learning latent priors.
problem Improving generation quality of deterministic AE models.
method Introducing flexibly learnable latent priors in WAEs to optimize the latent distribution.
result FlexAE achieves state-of-the-art performance in AE-based generative models.
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
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.
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in netw…
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contain…
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.
Paper addresses variational inference issues in Bayesian neural networks.
problem Negative infinite ELBO for function-space priors in BNNs.
method Regularized KL divergence for well-defined function-space variational inference.
result Method provides competitive uncertainty estimates for BNNs.
Unsupervised representation learning via generative modeling is a staple to many computer vision applications in the absence of labeled data. Variational Autoencoders (VAEs) are powerful generative models that learn representations useful for data generation. However, due to inherent challenges in the training objectiv…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or -prior) which unifies objective Bayes and information-based inference. The -prior is chosen to make the marginal probability an unbia…
Medical image reconstruction is typically an ill-posed inverse problem. In order to address such ill-posed problems, the prior distribution of the sought after object property is usually incorporated by means of some sparsity-promoting regularization. Recently, prior distributions for images estimated using generative …
A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a \emph{relational regularization} on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the la…
Bayesian -regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations. Spike-and-slab (a.k.a. Bernoulli-Gaussian) priors are the gold standard f…
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
problem Discount regularization leads to poor performance in unevenly sampled data.
method Equivalence theorem showing discount regularization as a strong prior, setting regularization parameters locally for individual state-action pairs.
result Discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
Unified framework for data-driven priors in Bayesian inverse problems
problem Bayesian inverse problems
method Unified framework using score functions
result Evaluation of four data-driven priors
We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, "weight decay", regularization. Our results characterize a more intricate regularization effect at the level of the unit activat…
High-dimensional prediction is a challenging problem setting for traditional statistical models. Although regularization improves model performance in high dimensions, it does not sufficiently leverage knowledge on feature importances held by domain experts. As an alternative to standard regularization techniques, we p…
Deep neural networks (DNNs) often require good regularizers to generalize well. Currently, state-of-the-art DNN regularization techniques consist in randomly dropping units and/or connections on each iteration of the training algorithm. Dropout and DropConnect are characteristic examples of such regularizers, that are …
Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization appr…
RSAC improves lightweight continuous learning efficiency.
problem Excessive training time and memory usage in continuous learning.
method Regularized subspace approximation classifier with feature reduction and regularization.
result RSAC achieves more efficient continuous learning than prior methods.
No regularization needed for InLDL, achieving efficient and effective model.
problem InLDL struggles with performance degradation due to missing degrees.
method Proposes a model that uses label distribution as a prior, implicitly regularizing the learning process.
result Achieves competitive performance without explicit regularization.
New static vacuum metrics confirmed for near Euclidean boundary data.
problem Establishing sufficient conditions for near Euclidean boundary data in static vacuum metrics.
method Using new arguments from studying the conjecture for arbitrary static vacuum metrics.
result Any hypersurface in a dense subfamily is static regular.
The paper studies multi-view representation learning with generalization guarantees and a new regularizer.
problem Distributed multi-view representation learning with correct estimation at a decoder.
method Generalization bounds using relative entropy and MDL, data-dependent Gaussian mixture priors.
result Data-dependent Gaussian mixture priors lead to good performance and outperform existing methods.
The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the stan…
Soft diamond regularizers improve deep learning performance and sparsity.
problem Improving deep learning performance and sparsity of trained weights.
method New soft diamond synaptic weight priors based on thick-tailed symmetric alpha stable probability curves.
result Soft diamond regularizers outperform state-of-the-art methods in deep learning tasks.
Bayesian deep learning faces posterior collapse due to likelihood vs. prior competition.
problem Posterior collapse in Bayesian deep learning models.
method Identified competition between likelihood and prior regularization in a linear latent variable model.
result Posterior collapse is related to neural and dimensional collapse, suggesting a broader learning issue.
This research improves binary classification by balancing overfitting and generalization with a novel Bayesian approach.
problem Improving binary classification models to avoid overfitting and generalize well.
method Introduces a PAC-Bayes type learning rule with a balancing parameter λ to balance training error and KL divergence to a prior.
result A choice of λ ensures uniformly vanishing excess loss, even in the agnostic case, by under-regularizing or over-regularizing appropriately.
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.
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistica…
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
Maximum Entropy competes with Maximum Likelihoodphysics.data-an
MAXENT method outperforms ML in sparse data with specific prior correlations.
problem Evaluating MAXENT method's validity limits and comparing it with ML.
method Bayesian decision theory, Dirichlet density, KL distance, regularized maximum likelihood.
result MAXENT can outperform ML in sparse data with specific prior correlations.
Prior domain knowledge can greatly help to learn generative models. However, it is often too costly to hard-code prior knowledge as a specific model architecture, so we often have to use general-purpose models. In this paper, we propose a method to incorporate prior knowledge of feature relations into the learning of g…
On parameters transformations for emulating sparse priors using variational-Laplace inferencestat.ML
So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined, i.e. when number of model parameters is much higher than the number of data point…
New method uses generative priors for compressive sensing with sparse solutions.
problem Fundamental linear inverse problem in compressive sensing.
method Sparse Bayesian learning with conditional Gaussianity.
result Ability to learn from few compressed and noisy samples without optimization.
GOAT improves attention mechanisms by learning better priors.
problem Standard attention mechanisms use a naive uniform prior, limiting flexibility and generalization.
method GOAT introduces a trainable, continuous prior that replaces the uniform assumption, maintaining compatibility with optimized kernels.
result GOAT avoids representational trade-offs and learns an extrapolatable prior that combines positional flexibility with length generalization.
We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by cross validation. Then we formulate network inference as a matrix completion problem…
New method uses diffusion models to solve inverse problems.
problem Solving ill-posed inverse problems with powerful priors.
method Formulate posterior sampling as a regularized Wasserstein gradient flow in latent space.
result Demonstrates improved performance on standard benchmarks.
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforc…
Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Predictionstat.ML
Bayesian Neural ODEs improve vessel trajectory prediction with better uncertainty estimates.
problem Challenges in predicting vessel trajectories from irregular AIS data.
method Adopted a Gaussian process (GP) kernel-based prior on the vector field evaluated at measurement points, combined with probabilistic multiple shooting for long trajectories.
result Improved accuracy and uncertainty quantification in vessel trajectory predictions.
This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.
problem Guaranteed tensor recovery with theoretical guarantees for low-rank and smoothness priors.
method Developed a new regularization term that combines low-rankness and smoothness priors, proving exact recovery guarantees.
result Rigorously proved exact recovery guarantees for tensor completion and tensor robust principal component analysis.
We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any…
Model-based free-breathing cardiac MRI reconstruction using deep learned \& STORM priors: MoDL-STORMcs.LG
We introduce a model-based reconstruction framework with deep learned (DL) and smoothness regularization on manifolds (STORM) priors to recover free breathing and ungated (FBU) cardiac MRI from highly undersampled measurements. The DL priors enable us to exploit the local correlations, while the STORM prior enables us …
Path regularization improves GFlowNets exploration and generalization.
problem Improving GFlowNets exploration and generalization.
method Path regularization based on optimal transport theory.
result Path regularization enhances GFlowNets to generate more diverse and novel candidates.
New FGSPCA method captures grouping and sparse structures in PCA without prior info.
problem Capture grouping and sparse structures in PCA without prior info.
method Truncated regularization with alternating algorithm.
result FGSPCA method reduces model complexity and increases interpretability.
Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in which units in the network are represented by latent variables, and the weights b…