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
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
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48 results for “posterior regularisation”
We introduce a framework for Continual Learning (CL) based on Bayesian inference over the function space rather than the parameters of a deep neural network. This method, referred to as functional regularisation for Continual Learning, avoids forgetting a previous task by constructing and memorising an approximate post…
New method regularizes deep networks using generative models.
problem Improving accuracy and uncertainty calibration in deep networks.
method Learn a generative model of all activations, insert imputed values during training, and condition posteriors on hidden layers.
result Higher test accuracy and lower cross-entropy compared to standard baselines.
Bayesian neural networks improve uncertainty quantification with unlabelled data.
problem Over-confidence in predictions on covariate-shifted data.
method Approximate Bayesian inference using posterior regularisation with pseudo-labels from unlabelled data.
result Significant improvement in uncertainty quantification accuracy on covariate-shifted data.
This paper improves inverse problem solving with weakly convex regularisers and proves convergence.
problem Improving solution methods for inverse problems.
method Generalised formulation of convergent regularisation using weakly convex regularisers, and proof of convergence for primal-dual hybrid gradient method.
result Proves convergence of primal-dual hybrid gradient method for variational problems and shows improved performance with IWCNNs.
GNIs induce a regulariser that penalizes high-frequency components in neural network activations.
problem Understanding the regularizing effect of Gaussian noise injections on neural network activations.
method Deriving the explicit regularizer by marginalizing out injected noise and analyzing its effect in the Fourier domain.
result GNIs induce a regularizer that produces calibrated classifiers with large margins.
Generalised regularisation equals robustness for exotic function classes.
problem Adversarial examples highlight the need for robust models in exotic function classes.
method Equality result linking distributional robustness and Lipschitz regularisation.
result Certified robustness of Lipschitz-regularised models with mild assumptions.
A Python package solves source duplication in single channel LVMs using spectral regularisation.
problem Source duplication in LVMs hampers their practical use in single channel applications.
method Spectral regularisation term added to address source duplication issue.
result Spectral regularisation framework enables easier investigation and utilisation of LVMs.
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is the core of kernel methods in machine learning as it makes th…
We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regulari…
On the Interpretability of Regularisation for Neural Networks Through Model Gradient Similaritystat.ML
New framework monitors neural network training and reveals regularisation mechanisms.
problem Overfitting in neural networks and the need for explicit regularizers.
method Model Gradient Similarity (MGS) framework to measure and monitor regularisation.
result Explicit regularizers increase Model Gradient Similarity (MGS).
This work uncovers algorithm-dependent regularisation in diffusion models.
problem Understanding and improving generalisation in high-dimensional diffusion models.
method Algorithmic stability and score stability analysis.
result Identifies multiple sources of implicit regularisation unique to diffusion models.
Unified framework reduces NFEs for inverse problems.
problem High computational costs and degraded reconstruction quality in existing LDM-based inverse solvers.
method Consistency Regularised Gradient Flows for posterior sampling and prompt optimization.
result Significantly reduced computational cost with state-of-the-art performance.
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and ext…
We propose a probabilistic framework to directly insert prior knowledge in reinforcement learning (RL) algorithms by defining the behaviour policy as a Bayesian posterior distribution. Such a posterior combines task specific information with prior knowledge, thus allowing to achieve transfer learning across tasks. The …
New method prevents deep learning forgetting past by remembering key examples.
problem Catastrophic forgetting in continual learning.
method Functional regularisation using Gaussian Process formulation.
result Achieves state-of-the-art performance on benchmarks.
A new measure helps compute suboptimality in entropy-regularized methods.
problem Computing suboptimality in entropy-regularized variational objectives when unnormalised densities are unavailable.
method Introduced 'kernel gradient discrepancy' (KGD) to compute suboptimality explicitly.
result KGD characterizes kernel Stein discrepancy (KSD) in the standard Bayesian context and measures variational gradient size.
This paper shows RL with KL penalties is equivalent to Bayesian inference for fine-tuning LMs.
problem Fine-tuning large language models to avoid undesirable features.
method Analyzed KL-regularized RL and showed it's equivalent to variational inference.
result KL-regularized RL avoids distribution collapse and is more insightful as Bayesian inference.
Implicit regularisation in stochastic gradient descent: from single-objective to two-player gamesstat.ML
Novel approach finds implicit regularisation in two-player games using BEA.
problem Understanding implicit regularisation in two-player games.
method Using backward error analysis to construct continuous-time flows with gradient-eligible vector fields.
result Identifies new implicit regularisation effects in two-player games.
Noise regularisation in deep nets makes them behave like Gaussian processes.
problem Understanding the behavior of noise-regularized deep neural networks as Gaussian processes.
method Analyzing the impact of noise regularisation on neural network Gaussian processes (NNGPs) and relating their behavior to signal propagation theory.
result Best performing NNGPs have kernel parameters corresponding to a specific initialisation scheme.
Regularization preserves topological data structure in autoencoders.
problem Ensuring topological data structure preservation in autoencoders.
method Regularization using Legendre nodes to preserve manifold embedding.
result Regularized autoencoders ensure one-to-one embedding of data manifolds.
Regularisation improves ML classifier stability against poisoning attacks.
problem Poisoning attacks degrade ML algorithms' performance; current attacks ignore hyperparameters.
method Proposed a multiobjective bilevel optimisation problem to consider hyperparameter effects.
result regularisation enhances learning algorithm stability and mitigates poisoning attacks.
Investigates gradient descent dynamics and introduces new regularisation methods.
problem Understanding and mitigating gradient descent instabilities and interactions with smoothness regularisation.
method Derives continuous-time flows to account for discretisation drift, constructs learning rate schedules and regularisers.
result New regularisation methods improve performance in reinforcement learning.
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
In this work we explore a straightforward variational Bayes scheme for Recurrent Neural Networks. Firstly, we show that a simple adaptation of truncated backpropagation through time can yield good quality uncertainty estimates and superior regularisation at only a small extra computational cost during training, also re…
(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stabilitycs.LG
Study on GD and SGD over diagonal networks, focusing on stepsizes and regularisation.
problem Understanding the impact of stochasticity and large stepsizes on gradient descent and SGD solutions.
method Investigation of GD and SGD over diagonal linear networks with macroscopic stepsizes, proving convergence and characterizing solutions.
result Large stepsizes consistently benefit SGD for sparse regression problems, but can hinder GD recovery of sparse solutions, especially in the edge of stability regime.
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logari…
This work shows how penalising bias terms in norm regularisation leads to sparse solutions.
problem Understanding the relation between parameter norm regularization and the sparsity of neural network solutions.
method Analyzes one hidden ReLU layer networks with unidimensional data, showing the norm required for function representation and the importance of the bias term's norm.
result Penalising the bias terms in regularisation leads to sparse solutions, enforcing the uniqueness and sparsity of the minimal norm interpolator.
Regularizes ML algorithms for robust multivariate analysis against distribution shifts.
problem Ensuring robustness of multivariate analysis algorithms against distribution shifts.
method Integrates a causal regularisation term into the loss function of multivariate analysis algorithms.
result Demonstrates improved out-of-distribution generalisation with reduced-rank regression and partial least squares.
Study on how noise and variation-norm regularisation help shallow ReLU networks use fewer neurons.
problem Understanding how shallow ReLU networks use a finite number of neurons in the infinitely wide limit.
method Analysis of two regularisation strategies: noise injection and variation-norm.
result Both regularisation methods minimize functions with a finite number of neurons, regardless of overparametrisation.
We showcase how dropout variational inference can be applied to a large-scale deep learning model that predicts price movements from limit order books (LOBs), the canonical data source representing trading and pricing movements. We demonstrate that uncertainty information derived from posterior predictive distributions…
This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.
problem Designing RL algorithms to balance exploration and exploitation in noisy environments.
method Entropy regularisation in two formulations: exploratory control and proximal policy update.
result Regret of for both learning algorithms over episodes.
Paper studies particle method for LSV model calibration, proving convergence and error bounds.
problem Calibration of local-stochastic volatility models with open well-posedness question.
method Regularized Euler--Maruyama scheme for particle approximation of McKean--Vlasov dynamics.
result Strong convergence of the Euler--Maruyama scheme with rate 1/2 in step-size.
A robust loss for anomaly mitigation and unsupervised contamination classification
problem Detecting and mitigating contamination in supervised and unsupervised settings
method Neural Bayesian Anomaly Mitigation (NBAM)
result Recovering the structure of contamination and identifying label-flip pairs
Effective regularisation of neural networks is essential to combat overfitting due to the large number of parameters involved. We present an empirical analogue to the Lipschitz constant of a feed-forward neural network, which we refer to as the maximum gain. We hypothesise that constraining the gain of a network will h…
Characterizes uncertainty in high-dimensional linear classification models.
problem Assessing uncertainty in high-dimensional linear classification models.
method Approximate message passing algorithm for posterior marginals, closed-form formula for joint statistics.
result Closed-form formula for joint statistics between logistic classifier, Bayesian uncertainty, and ground-truth probit uncertainty.
A trade-off exists between reconstruction quality and the prior regularisation in the Evidence Lower Bound (ELBO) loss that Variational Autoencoder (VAE) models use for learning. There are few satisfactory approaches to deal with a balance between the prior and reconstruction objective, with most methods dealing with t…
New insights into how neural networks learn features, especially when they are very wide.
problem Understanding how gradient flow in wide neural networks selects solutions, especially in the feature-learning regime.
method Axiomatizing the canonical regularizer as a function-space energy and lift, and deriving geodesic ridge for the feature-learning regime.
result Gradient flow in feature-learning networks biases towards ridge regularization, distorting the inductive bias and damaging pretrained networks.
Study on neural networks with regularisation and its impact on training dynamics.
problem Understanding the dynamics of neural networks with regularization.
method Established explicit dynamics for neural networks with a regularizing term, linearizing around initialisation.
result The regularisation term modifies the standard NTK dynamics, leading to new insights into network training.
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to . Our approach is based on regularisations of the metric adapted to the causal structure.
Regularising for invariance to data augmentation improves machine learning models.
problem Improving generalization in machine learning models through data augmentation.
method Explicit regularisation to encourage invariance at the level of individual model predictions.
result Explicit regularisation improves generalization and equalizes performance differences between objectives.
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling…
Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the…
Unified understanding of three continual learning regularisation methods.
problem Maintaining knowledge of earlier tasks without re-accessing them.
method Three regularisation approaches: Elastic Weight Consolidation (EWC), Synaptic Intelligence (SI), and Memory Aware Synapses (MAS).
result EWC, SI, and MAS are linked to the same theoretical quantity, the square root of the Fisher Information.
New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.
problem Challenges in applying regularisation to the evolving mode of PARAFAC2.
method Alternating Direction Method of Multipliers (AO-ADMM) for PARAFAC2 tensor fitting.
result The proposed ADMM-based approach accurately recovers underlying components from simulated data.
The paper studies -positive currents and line bundles on complex manifolds.
problem Understanding -positive currents and their properties on complex manifolds.
method Introducing -plurisubharmonic functions, proving vanishing theorems, and regularisation theorems using viscosity solutions.
result Global and local regularisation theorems for -semi-positive currents.
Uncertainty-Based Smooth Policy Regularisation for Reinforcement Learning with Few Demonstrationscs.LG
SPReD uses uncertainty to decide imitation from demonstrations.
problem Learning from sparse rewards with few demonstrations.
method Ensemble methods to model Q-value distributions, probabilistic and advantage-based uncertainty quantification.
result Significant gains in reinforcement learning across multiple tasks.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).