Unified continuous diffusion model outperforms discrete alternatives in scalability and quality.
problem Continuous diffusion models were perceived as less scalable than discrete models.
method Reconstructed Plaid model and compared it with modern discrete DLMs, optimizing noise schedule and embeddings via likelihood.
result Unified continuous diffusion model (RePlaid) outperforms discrete models in compute efficiency and quality.
Paper proves method for calculating NML code length works for continuous models.
problem Uncertainty in calculating NML code length for continuous models.
method Introduced a novel decomposition approach based on the coarea formula to prove correctness for continuous cases.
result Method accurately calculates NML code length for continuous models.
Unified approach to continual learning using Bayesian methods.
problem Challenges in evaluating posterior approximations for continual learning.
method Introduces a new approximate Bayesian derivation of the continual learning loss, adapting the model itself by changing the likelihood term.
result Combines prior- and likelihood-focused methods into one objective, achieving better performance.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
VAIOM models financial returns using continuous input and categorical output.
problem Modeling continuous, noisy, and heterogeneous financial data.
method VAIOM is a decoder-only Transformer that separates input representation from output likelihood.
result VAIOM models outperform fixed single-bar LightGBM baseline in both Test halves.
New method balances multivariate model fitting for mixed likelihoods.
problem Multivariate models often fit only a subset of observed variables.
method Lipschitz standardization for data preprocessing.
result Lipschitz standardization leads to more accurate multivariate models.
We study asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, whi…
New method infers network couplings from spin trajectories in continuous time.
problem Inferring network couplings from observed spin trajectories in continuous time.
method Introducing latent variables to linearize and make likelihood quadratic, deriving EM and variational algorithms.
result Demonstrated performance on simulated data and biologically plausible network.
Paper develops unbiased gradient estimator for continuous-time models.
problem Estimating unbiased gradient of log-likelihood for continuous-time models.
method Doubly randomized scheme with coupled conditional particle filter (CCPF).
result Unbiased gradient estimate facilitates gradient-based algorithms.
Paper constructs conjugate pairs for Bayesian nonparametric models with continuous likelihoods.
problem Limited conjugate pairs for Bayesian nonparametric models with continuous likelihoods.
method Develops a general construction for prior, likelihood, and posterior in conjugate pairs for processes with Levy measure densities from positive exponential families.
result Demonstrates conjugacy for processes with Levy measure densities from positive exponential families.
POWSS simplifies Q-value estimation in POMDPs with continuous observations.
problem Lack of theoretical justification for online sampling-based algorithms in POMDPs with continuous observation spaces.
method Developed POWSS, a simplified algorithm that estimates Q-values accurately with high probability and can approach optimality with increased computational power.
result POWSS provides formal theoretical guarantees for Q-value estimation in POMDPs with continuous observations.
The study tackles modeling high-frequency financial data using continuous distributions, finding them inadequate.
problem Challenges in modeling high-frequency integer price changes with continuous distributions.
method Proposed a modified maximum likelihood estimation procedure to account for the discreteness of high-frequency price changes.
result Traditional GARCH models are not suitable for high-frequency data due to the discreteness of price changes.
Simple optimization method for Poisson likelihood models.
problem Optimizing Poisson likelihood models with non-Lipschitz continuity.
method Saddle point reformulation, gradient-based optimization, randomized block-decomposition.
result Gradient-based optimization with O(1/t) convergence rate for large-scale problems. Continuous neural networks using differential equations.
problem Training and optimizing neural networks with continuous-depth architectures.
method Parameterize derivative of hidden state using neural networks and solve differential equations.
result End-to-end training of continuous-depth models.
Paper develops methods for estimating and forecasting integer-valued trawl processes.
problem Estimation and forecasting of continuous-time integer-valued trawl processes.
method Composite likelihood methods, focusing on pairwise likelihood.
result Consistency and asymptotic normality of the estimator in the short memory case.
A new method learns quantization boundaries in continuous space using tessellation.
problem Mapping between discrete and continuous distributions is difficult.
method Constructs normalizing flows on convex polytopes with exact likelihood evaluations.
result Improves likelihood evaluation and quantization learning across various data modalities.
Neural SDEs model continuous sequences using neural networks.
problem Modeling continuous-time dynamics in sequence data.
method Interprets time-series as samples from a continuous dynamical system, parameterized by Neural SDE.
result Demonstrates superior performance in diverse sequence modeling tasks.
Study on MLE growth rate for stable CIR process, proving consistency and normality.
problem Estimating the growth rate of a stable CIR process from continuous observations.
method Maximum likelihood estimation for a specific type of process.
result Strong consistency and asymptotic normality in subcritical and supercritical cases, asymptotic mixed normality in supercritical, open in critical case.
Paper proposes efficient training for normalizing flows in Boltzmann generators.
problem Training normalizing flows for Boltzmann generators is computationally challenging and unstable.
method Regression Training of Normalizing Flows (RegFlow) using ℓ2-regression. result RegFlow enables efficient and stable training of normalizing flows for Boltzmann generators.
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.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
A new method for binary ICA using non-stationary sources.
problem Independent component analysis of binary data.
method Linear mixing model in latent space, followed by binary observation model with non-stationary sources.
result Proves non-identifiability with few observed variables but identifies with more variables.
New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.
New CTRL algorithm adapts to varying problem difficulty.
problem Adapting to varying levels of problem difficulty in CTRL.
method MLE with a general function approximator, estimating state marginal density.
result Regret bound scales with reward variance and measurement resolution, independent of measurement strategy.
A new method learns continuous occupancy fields efficiently using the Ising model.
problem Efficiently learning continuous occupancy fields for robot navigation.
method Generalizes the Ising model to model continuous occupancy fields, using a unique kernel for range measurements.
result The method is computationally efficient and requires only a small number of hyperparameters.
This work studies the exact likelihood of DLVMs and its applications in inference.
problem The lack of attention to the exact likelihood of DLVMs and its implications for inference.
method Investigation of the properties of the exact likelihood, maximum likelihood estimation, and missing data imputation.
result The exact likelihood can be leveraged to ensure the existence of maximum likelihood estimates and improve missing data imputation.
FFJORD models generate complex distributions efficiently with unbiased density estimation.
problem Efficiently generating complex distributions with unbiased density estimation.
method FFJORD uses continuous-time invertible neural networks with Hutchinson's trace estimator for unbiased log-density estimation.
result FFJORD achieves state-of-the-art performance in high-dimensional density estimation, image generation, and variational inference.
Survival MDN uses invertible functions to speed up survival analysis models.
problem Training neural ODEs for survival analysis is computationally expensive.
method Survival MDN applies an invertible positive function to MDN outputs.
result Survival MDN outperforms or matches other models on concordance, Brier score, and log-likelihood.
A new normalizing flow models continuous stochastic processes efficiently.
problem Efficient modeling of continuous stochastic processes.
method Dynamic normalizing flows driven by Wiener process.
result Rich time series model with efficient computation of likelihoods and marginals.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.
Privacy-preserving continual learning for hospitals.
problem Forgetting old data when updating neural networks for privacy.
method Differentially private variational inference and generative models.
result Estimates likelihood of old data given current model.
Identifies interpretable generative model for multivariate data.
problem Black-box architectures of deep generative models are often unidentified and difficult to interpret.
method Introduces Deep Discrete Encoder (DDE) Copula, a hierarchical binary latent variable model inside a copula framework.
result Establishes conditions for identification of DDE copula parameters and proves posterior consistency.
New bounds for DPPs avoid spectral decomposition and enable inference.
problem Learning parameters of DPPs' kernel K is difficult due to spectral decomposition and intractable normalizing constant. method Derive cheap bounds on likelihood without spectral decomposition, enabling variational and MCMC inference.
result Cheap variational and moderately expensive MCMC inference methods for DPPs.
We improve Whittle likelihood estimates for stationary processes.
problem Biased parameter estimates from Whittle likelihood.
method De-biased Whittle likelihood method.
result Significant reduction in bias with improved computational efficiency.
Maximum likelihood estimation fails to be well-posed in Gaussian process regression.
problem Establishing well-posedness of maximum likelihood estimation in Gaussian process regression.
method Analyzing the conditions under which maximum likelihood estimation is not Lipschitz in the data with respect to the Hellinger distance.
result Maximum likelihood estimation is not well-posed in the noiseless data setting for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood.
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU) processes. This models are known to be substantially more flexible than Gaussian …
Estimates customer segments from continuous marketing data streams.
problem Analyzing large, continuously updated marketing data streams.
method oFMLR: online estimation of finite mixture of logistic regression models.
result oFMLR provides interpretable customer segment clustering.
New metrics improve learning of Gaussian networks.
problem Lack of suitable metrics for continuous Bayesian network learning.
method Introduce three-part minimum description length and renormalized normalized maximum likelihood metrics.
result Proposed metrics outperform BIC/AIC metrics in accuracy and convergence.
Study maximum likelihood estimators for a jump Heston model, proving consistency and normality.
problem Estimating drift parameters in a jump-type Heston model with non-Gaussian jumps.
method Asymptotic analysis of maximum likelihood estimators based on continuous observations.
result Strong consistency and asymptotic normality for most parameter values, weak consistency and mixed normality for one.
Proposes ABC method for discrete data, improving likelihood-free inference.
problem Discrete data likelihood-free inference problems.
method Population-based MCMC ABC framework with a new Markov kernel inspired by Differential Evolution.
result High potential and superiority of the new Markov kernel demonstrated.
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
Develops a framework for modeling set-valued data in continuous-time.
problem Handling sequences where each event is associated with a set of items.
method General framework for modeling set-valued data, developed inference methods, and importance sampling techniques.
result Orders-of-magnitude improvements in efficiency for probabilistic queries over direct sampling.
Paper solves inverse problem in continuous Markov fields using Bethe approximation and loopy belief propagation.
problem Solving the inverse problem in Markov random fields with non-parametric pair-wise energy function.
method Loopy belief propagation and orthonormal function expansion to approximate the partition function and solve functional optimization.
result Analytic solution to inverse problem in continuous Markov fields.
Researchers develop a method to learn CTBN structure using penalized maximum likelihood.
problem Learning the structure of continuous-time Bayesian networks (CTBNs) when the dependence structure is unknown.
method Penalized maximum likelihood method.
result The algorithm can accurately identify the network structure with high probability under certain conditions.
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distributio…
Paper introduces new methods for modeling categorical data.
problem Training generative models on categorical data like text and segmentation.
method Argmax Flows and Multinomial Diffusion models.
result Models outperform existing methods in log-likelihood.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.