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.
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…
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 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.
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…
New method uses neural networks to efficiently approximate Bayesian inference for complex models.
problem Efficiently approximating Bayesian inference for complex models with varying temperatures.
method Fully amortized neural posterior estimator trained on a single forward pass.
result Achieves competitive posterior approximations across various temperatures and benchmarks.
Study normal tempered stable processes for energy derivative pricing.
problem Pricing energy derivatives with spot price models.
method Specified statistical properties, derived non-arbitrage conditions, developed efficient algorithm for trajectory generation.
result Validated pricing models for various energy contracts.
An infinite parallel tempering bouncy particle sampler improves sampling efficiency for multimodal distributions.
problem Sampling from complex posterior distributions with high accuracy and efficiency.
method Introduced an infinite parallel tempering bouncy particle sampler (BPS-PT) to accelerate convergence.
result Demonstrated improved sampling efficiency for multimodal distributions through numerical simulations.
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.
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.
New model captures time-varying volatility with stochastic exponential tails.
problem Capturing time-varying volatility and stochastic skewness in financial markets.
method Normal Tempered Stable distribution with time-varying parameter.
result Model better explains market option prices with stochastic exponential tails.
Study prices energy derivatives using specific stochastic processes.
problem Pricing energy derivatives in markets driven by specific stochastic processes.
method Calculated characteristic functions, derived non-arbitrage conditions, and developed efficient algorithms for simulation.
result Developed methods for pricing various energy contracts.
The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.
problem Mitigating left tail risk in multi-asset portfolios.
method Proposes a Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) for portfolio optimization.
result Optimal portfolios with tail risk measures outperform standard deviation-based portfolios and equally weighted portfolios in various performance metrics.
We propose a new sampling method, the thermostat-assisted continuously-tempered Hamiltonian Monte Carlo, for Bayesian learning on large datasets and multimodal distributions. It simulates the Nosé-Hoover dynamics of a continuously-tempered Hamiltonian system built on the distribution of interest. A significant advantag…
Enhances gradient-based discrete samplers with parallel tempering for multimodal distributions.
problem Local minima in high-dimensional, multimodal discrete distributions.
method Combines parallel tempering with discrete Langevin proposal, using Metropolis criterion for swaps.
result Significantly faster mixing and better sampling from complex distributions.
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.
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.
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.
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…
Improved PDMP samplers for multi-modal distributions using tempering.
problem Struggles of PDMP samplers with multi-modal or heavy-tailed distributions.
method Tempering PDMPs by interpolating between a tractable and posterior distribution.
result PDMP samplers can be improved to sample from multi-modal distributions.
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…
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.
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.
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 method trains neural samplers without simulation, but fails due to mode collapse.
problem Training neural samplers without simulation.
method Time-dependent normalizing flow with Langevin preconditioning.
result Langevin preconditioning is crucial for avoiding mode collapse.
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.
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.
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…
A fast Monte Carlo method for additive processes and option pricing.
problem Efficiently pricing path-dependent options with additive processes.
method Developed a fast Monte Carlo scheme for additive processes, analyzing and reducing numerical error sources.
result Shows significant reduction in error (1 bp or below) for pricing path-dependent options.
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.
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…
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.
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.
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 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…
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…
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have provided "beyond worst-case" guarantees for such settings. For log-c…
FlowVAT improves variational inference for multi-modal distributions.
problem Mode-seeking behavior and collapse in variational inference for complex posteriors.
method Conditional tempering approach for normalizing flow variational inference.
result FlowVAT outperforms traditional and adaptive annealing methods in multi-modal distributions, finding more modes and achieving better ELBO values.
Minimum Description Length prevents overfitting in noisy data.
problem Learning from noisy data with overfitting risk.
method Minimum Description Length learning rule with tempered guarantees.
result Tempered agnostic finite sample learning guarantees and asymptotic behavior characterization.
Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.
problem High-dimensional multimodal posterior distributions in deep learning.
method Cyclical MCMC framework that tracks tempered versions of the target distribution over time.
result Cyclical MCMC converges to the target distribution under fast mixing kernels but fails in slow mixing cases.