Improved model-based estimation through tempered Bayes filter.
problem Improving predictive accuracy in partially-observable stochastic systems.
method Developed tempered Bayes filter combining likelihood and full posterior tempering.
result Tempered Bayes filter achieves improved predictive performance over the Bayes filter baseline.
Paper introduces deterministic EM approximations for non-convex likelihood functions.
problem Deterministic approximations for the E-step of EM algorithm are lacking.
method Developed a theoretical framework for deterministic approximations, analyzed Riemann sums and tempered EM.
result Proved convergence guarantees for deterministic approximations and new non-trivial temperature profiles.
Cold posteriors in BNNs harm performance, likely due to incorrect likelihood.
problem Cold posteriors in Bayesian neural networks degrade performance.
method Developed a generative model explaining cold posteriors and matched it to the tempered likelihoods.
result Cold posteriors are a result of using the wrong likelihood for image classification datasets.
Restricted Boltzmann Machines (RBM) have attracted a lot of attention of late, as one the principle building blocks of deep networks. Training RBMs remains problematic however, because of the intractibility of their partition function. The maximum likelihood gradient requires a very robust sampler which can accurately …
The paper uses FRFT to fit GTS distribution to asset returns.
problem Modeling asset returns with GTS distribution.
method Fractional Fourier Transform (FRFT) for fitting.
result GTS distribution fits SPY ETF and Bitcoin BTC returns.
Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been established as a safer way to do updates from prior to posterior in the presence of mod…
Bayesian classification improves with explicit aleatoric uncertainty.
problem Lack of aleatoric uncertainty representation in Bayesian classification.
method Explicitly account for aleatoric uncertainty using a Dirichlet observation model.
result Explicit aleatoric uncertainty improves performance of Bayesian neural networks.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This approach uses a decreasing te…
The paper fits a seven-parameter GTS distribution to financial data.
problem Nonexistence of GTS probability density function makes MLE inadequate.
method Used fractional Fourier transform to circumvent MLE and provide good parameter estimation.
result The GTS distribution fits financial data significantly better than other models.
Due to the need for robust uncertainty quantification, Bayesian neural learning has gained attention in the era of deep learning and big data. Markov Chain Monte-Carlo (MCMC) methods typically implement Bayesian inference which faces several challenges given a large number of parameters, complex and multimodal posterio…
We introduce thermodynamic response functions for singular Bayesian models.
problem Singular Bayesian models violate regular asymptotics due to non-identifiability and degenerate Fisher geometry.
method Posterior tempering induces thermodynamic response functions, linking WAIC, WBIC, and singular fluctuation.
result WAIC, WBIC, and singular fluctuation are unified within a thermodynamic response framework.
In this paper we demonstrate that tempering Markov chain Monte Carlo samplers for Bayesian models by recursively subsampling observations without replacement can improve the performance of baseline samplers in terms of effective sample size per computation. We present two tempering by subsampling algorithms, subsampled…
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
Improved continual learning method using variational inference and FiLM layers.
problem Training models on new tasks and datasets in an online fashion.
method Generalized Variational Continual Learning (GVCL) with likelihood-tempering and FiLM layers.
result GVCL outperforms existing baselines in both small and large datasets, providing better calibration.
The paper connects tempering and entropic mirror descent for sampling.
problem Sampling from a target distribution with known unnormalized density.
method Establishes the connection between tempering SMC and entropic mirror descent, deriving convergence rates and geometric insights.
result Tempering SMC iterates correspond to entropic mirror descent on the reverse KL divergence, providing new optimization perspectives.
Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally efficient Gibbs sampling procedures are crippled by poor mixing. In this work w…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their p-var…
The complex and computationally expensive nature of landscape evolution models pose significant challenges in the inference and optimisation of unknown parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed para…
We introduce a new distance metric for non-linear embeddings of Tempered Exponential Measures.
problem Non-linear embeddings of Tempered Exponential Measures (TEMs).
method Parameterization of finite discrete TEMs via Legendre functions, introducing tempered Hilbert co-simplex distance.
result Established a generalization of the Hilbert log cross-ratio simplex distance to a tempered Hilbert co-simplex distance.
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…
Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliar…
Geometric tempering fails for Langevin dynamics, proving convergence limits.
problem Proving convergence and limitations of geometric tempering for Langevin dynamics.
method Theoretical investigation of geometric tempering using Langevin dynamics.
result Geometric tempering can lead to exponential time convergence and poor functional inequalities.
Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
New adaptive temperature selection improves parallel tempering efficiency.
problem Enhancing mixing in multi-modal distributions using parallel tempering.
method Adaptive temperature selection using policy gradient approach.
result Lower integrated autocorrelation times achieved compared to traditional methods.
New priors improve Bayesian neural networks without cooling.
problem Bayesian neural networks underfit on clean datasets.
method Introduce DirClip and confidence priors to replace cooling.
result DirClip and confidence priors outperform cold posterior.
Improves neural network performance by dynamically adjusting model weights based on source reliability.
problem Training neural networks on data from unreliable sources leads to poor performance.
method Dynamic re-weighting strategy using likelihood tempering to adjust model weights based on estimated source reliability.
result Significant improvement in model performance when trained on mixtures of reliable and unreliable data sources.
New insights on Bayesian models show stochasticity doesn't always improve accuracy.
problem The impact of stochasticity in Bayesian models and the role of temperature parameters.
method Detailed investigation, empirical testing, and PAC-Bayesian analysis.
result Stochasticity does not generally improve test accuracy and the coldest temperature is often optimal.
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
We offer new formulas for European option pricing under tempered stable processes.
problem Pricing European options under tempered stable processes.
method Series expansions for tempered stable densities and European option prices.
result Our formulas are hyperparameter-free and competitive with traditional methods.
New financial models use tempered stable subordination for better correlation dynamics.
problem Building financial models with better correlation dynamics.
method Introducing tempered stable Sato subordinators and additive inhomogeneous processes.
result The new process has time-dependent correlation, improving fit for financial data.
Polynomial mixing times for simulated tempering in mixture sampling problems.
problem Sampling from mixtures of log-concave distributions with location shifts.
method Conductance decomposition applied to an auxiliary Markov chain on an augmented space.
result First polynomial-time guarantee for simulated tempering with MALA.
Improved MCMC sampling for expensive, irregular likelihoods.
problem Bayesian inference challenges with irregular, expensive likelihoods.
method Adapt subset samplers, introduce data-driven proxies, adaptive controller.
result Improved HINTS algorithm achieves best sampling error in fixed budget.
We prove overfitting in minimal and random NNs, tempering the effect.
problem Overfitting in minimal and random neural networks.
method Analyzing binary weight fitting to noisy data, proving overfitting is tempered.
result The overfitting of minimal and random neural networks is tempered.
New framework uses tempered optimism to handle imperfect experts in online learning.
problem Challenges of implicit optimism in practical online learning environments.
method Introduces tempered optimism as a framework for online non-convex learning, modifies existing algorithms.
result Demonstrates tempered optimism as a fruitful paradigm for online non-convex learning.
Geometric tempering improves sampling from distributions, with exponential convergence rates.
problem Sampling from probability distributions using gradient flow dynamics.
method Geometric tempering of the target distribution in Wasserstein and Fisher-Rao gradient flows.
result Exponential convergence in continuous and discrete time for geometric tempering.
New method improves sampling from complex, multi-peaked distributions.
problem Sampling from high-dimensional, multimodal distributions using HMC.
method Combines tempered HMC with automatic tuning strategies.
result Demonstrates more effective scaling with dimension than adaptive methods.
This work tackles GAN training instability through parallel tempering.
problem Training instability and mode collapse in GANs.
method Introduces a parallel tempering framework to stabilize GAN training.
result Significantly reduces gradient variance and improves training efficiency.
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure between components are investigated. We discuss a random number generating procedu…
In this short note, we show how the parallel adaptive Wang-Landau (PAWL) algorithm of Bornn et al. (2013) can be used to automate and improve simulated tempering algorithms. While Wang-Landau and other stochastic approximation methods have frequently been applied within the simulated tempering framework, this note demo…
Improved lower bound for parallel tempering's mixing time.
problem Slow convergence and mixing in multimodal target distributions.
method Presented a new lower bound for the spectral gap of parallel tempering.
result Improved the best existing bound on spectral gap with polynomial dependence on parameters.
Develops a Monte Carlo algorithm for tempered stable process extrema.
problem Calculating the extrema of exponentially tempered Lévy processes.
method Novel Monte Carlo algorithm based on increments of the process.
result Geometrically fast convergence and optimal computational complexity.
New method estimates tempered stable Lévy models with high accuracy.
problem Estimating volatility and jump intensity of tempered stable Lévy processes.
method Iterative method combining Truncated Realized Quadratic Variations and small-time approximations.
result Method outperforms existing alternatives in various scenarios.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
New theorem improves spectral gap for sampling from mixture distributions.
problem Sampling from multimodal distributions with simulated tempering.
method Introduced a decomposition theorem for the restricted spectral gap of simulated tempering.
result Lower bound on the restricted spectral gap for mixture distributions.
New subgroup found in Lie groups with unusual properties.
problem Finding discrete subgroups with specific properties in Lie groups.
method Constructing a specific subgroup of a higher rank Lie group.
result Found a new subgroup that is dense, discrete, non-lattice, and non-tempered.
We define the spaces of Schwartz functions, tempered functions and tempered distributions on manifolds definable in polynomially bounded o-minimal structures. We show that all the classical properties that these spaces have in the Nash category, as first studied in Fokko du Cloux's work, also hold in this generalized s…
DSPM models control noise volatility, improving financial data analysis.
problem Financial returns exhibit volatility clustering, challenging traditional models.
method DSPM uses a tempered-stable subordinator to control noise volatility, preserving kurtosis and autocorrelation.
result DSPM models accurately capture volatility clustering and noise mechanisms.