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 formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximatio…
Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Mo…
Paper proposes a method to estimate consumer valuations from bundle sales data.
problem Estimating consumer valuations from bundle sales data using classical methods is challenging.
method Proposes an approach using EM algorithm and Monte Carlo simulation to estimate consumer valuations from bundle sales data.
result The approach can recover the distribution of consumers' valuations and is robust to unobserved no-purchases and clustered market segments.
We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite samples. Because EM sits on a rigorous statistical foundation and has been thorough…
New Hamiltonian Monte Carlo method for non-canonical dynamics.
problem Incompatibility of canonical symplectic structure with non-canonical dynamics.
method Developed a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures with implicit integration.
result Non-canonical Hamiltonian Monte Carlo provides sampling advantages.
The paper develops a method to learn SDE drift functions from sparse, noisy data.
problem Learning SDE drift functions from sparse and noisy data without strong structural assumptions.
method Data-driven approach using a penalized negative log-likelihood functional over RKHS, with an EM algorithm employing SMC for approximations.
result The method enables accurate estimation of SDE drift functions in low-data regimes.
New algorithm improves latent variable model estimation.
problem Estimating parameters in latent variable models.
method Jarzynski-adjusted Langevin algorithm (JALA) for SMC methods.
result JALA-EM provides maximum marginal likelihood estimate.
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
Enhances deep learning models for anomaly detection in time series data.
problem Anomalies in time series data corrupt performance of models.
method Monte Carlo EM for inferring anomaly indicators during training.
result Improves model performance on nominal data and anomalous points.
We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are functions of the parameters being sampled. This leads to significant complexiti…
MissDAG addresses causal discovery with missing data using imputation and EM.
problem Causal discovery with missing data in incomplete observational studies.
method MissDAG uses EM framework to maximize likelihood of visible data, leveraging ANMs and Monte Carlo EM for approximations.
result MissDAG outperforms two-step imputation and causal discovery methods.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
Study on interest rate model with jumps, proving strong convergence in simulations.
problem Analytical solutions for complex interest rate models with jumps are difficult.
method Employed truncated Euler-Maruyama techniques to prove strong convergence.
result Justified strong convergence for Monte Carlo calibration and valuation.
Two-Timescale EM Methods improve EM for nonconvex models.
problem Nonconvex latent variable models are challenging for EM.
method Two-stage stochastic updates to handle nonconvex optimization.
result Global convergence for nonconvex objective functions.
New approach improves AI's handling of incomplete data.
problem Improving AI's ability to work with incomplete data.
method Proposes a new likelihood-free EM algorithm for faster, more efficient inference.
result More statistically efficient than masking approach and faster than conventional EM.
Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
New EM algorithm improves deep generative network training.
problem Training deep generative networks with complex posterior and likelihood distributions.
method Derive analytical posterior and marginal distributions using CPA property, derive analytical EM algorithm.
result EM training yields higher likelihood than Variational Autoencoders (VAEs).
Study improves risk evaluation timing with right-censored reporting delays.
problem Improving risk evaluation under short observation windows due to administrative censoring.
method Jointly models parametric hazards for event and reporting processes, uses Monte Carlo expectation-maximization algorithm, and proposes transfer-learning procedure.
result Improves accuracy of timely risk evaluation under administrative censoring.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from parallel implementations, and consequently Monte Carlo has become a focal point …
New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.
problem Sampling from distributions with nonsmooth convex composite potentials.
method Leveraging Bregman--Moreau envelopes and proximal operators in mirror descent.
result Efficiency in sampling from nonsmooth distributions, extending existing methods.
ML-EM method speeds up diffusion model sampling.
problem Efficiently sampling from complex diffusion models.
method Multilevel Euler-Maruyama method with UNet approximations.
result Polynomial speedup in sampling from diffusion models.
Stochastic EM with biased MCMC improves inference stability.
problem Intractable E-step in EM algorithm.
method Stochastic approximation with biased MCMC.
result ULA is more stable and sometimes faster than MALA.
Hamiltonian Monte Carlo converges to target distributions under mild conditions.
problem Establishing convergence of Hamiltonian Monte Carlo algorithms.
method Analyzing Lq convergence for Hamiltonian Monte Carlo under mild conditions. result Outputs converge to target distributions under specified conditions.
We propose an expectation-maximization-like(EMlike) method to train Boltzmann machine with unconstrained connectivity. It adopts Monte Carlo approximation in the E-step, and replaces the intractable likelihood objective with efficiently computed objectives or directly approximates the gradient of likelihood objective i…
Improves Monte-Carlo simulations for consistent mean and variance.
problem Artificial randomness in running mean calculations.
method Combining running mean and variance with accurate summing.
result Increased accuracy and robustness of Monte-Carlo estimates.
New algorithms improve Langevin Monte Carlo efficiency.
problem High computational cost of classical Langevin Monte Carlo.
method Integrates ensemble feature into LMC, constraining gradient approximations.
result Constrained Ensemble Langevin Monte Carlo reduces gradient computation.
Quantum algorithm speeds up financial option pricing.
problem Optimizing stopping times in stochastic processes for finance.
method Combines quantum computing techniques with LSM for optimal stopping.
result Achieves nearly quadratic speedup in runtime.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
problem Improving state-space radio interferometric imaging in the presence of heavy-tailed noise
method Stochastic Approximation Expectation Maximization
result Significant improvement in reconstruction fidelity and robustness to radio-frequency interference
This paper reviews various sampling methods from statistics and machine learning.
problem Addressing sampling methods in statistics and machine learning.
method Explains and reviews simple random sampling, bootstrapping, stratified sampling, cluster sampling, multistage sampling, network sampling, snowball sampling, and sampling from cumulative distribution function.
result Summarizes characteristics, pros, and cons of different sampling methods.
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p…
Quantum computing offers a quadratic speedup for estimating non-linear functionals.
problem Estimating non-linear functionals of probability distributions.
method Proposes a quantum-inside-quantum Monte Carlo algorithm for a broad class of non-linear estimation problems.
result Achieves a quadratic speedup for non-linear estimation problems, including nested conditional expectations and stochastic optimization.
Paper improves Monte Carlo sampling with new theoretical insights and methods.
problem Improving Monte Carlo sampling for variance reduction.
method Theoretical analysis of negatively dependent random variables and novel extensions using number theory and particle algorithms.
result Near-Orthogonal Monte Carlo (NOMC) consistently outperforms Orthogonal Monte Carlo (OMC) in various applications.
The paper proposes a new method to approximate Wasserstein-Fisher-Rao flows using Monte Carlo techniques.
problem Sampling from probability distributions and minimizing Kullback-Leibler divergence.
method Sequential Monte Carlo approximations of Wasserstein-Fisher-Rao gradient flows.
result The proposed method outperforms other Monte Carlo algorithms in certain conditions.
The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH paramete…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has led to some fundamentally new Monte Carlo algorithms which can be used to sample f…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of th…
Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.
problem Analyzing Gibbs and Langevin Monte Carlo in overparameterized interpolation regime.
method Data-dependent bounds and stability under approximation with Langevin Monte Carlo.
result Generalization is signaled by small training errors in noisy regime, with bounds stable under approximation.
Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in general performing exact inference requires all of the data to be processed at eac…
A new Monte Carlo sampling method derived from reverse diffusion.
problem Sampling from complex distributions, especially multi-modal ones.
method Transforming score matching into mean estimation; estimating means of regularized posterior distributions.
result rdMC can approximate sampling with any desired accuracy and is significantly faster than MCMC for complex distributions.
New Langevin algorithms improve sampling efficiency in high dimensions.
problem Sampling from log-concave and smooth distributions in high dimensions.
method Combining splitting and accurate integration methods for P-th order Langevin dynamics. result LMC algorithms converge faster with better dimension dependence as P increases. Study Langevin Monte Carlo for sampling non-log-concave distributions.
problem Sampling from non-log-concave distributions, especially Gaussian mixtures.
method Discretizations of overdamped Langevin diffusions.
result Numerical simulations compare Langevin Monte Carlo algorithms' performance.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5/2-order L2-accuracy in approximating Hamiltonian flows. SBMC method improves uncertainty estimation in deep learning models.
problem Improving uncertainty quantification in deep learning models.
method A scalable Bayesian Monte Carlo method using a model and parallel SMC/MCMC algorithm.
result SBMC achieves comparable or better accuracy and improved uncertainty quantification compared to state-of-the-art methods.