Diffusion models improve creativity by smoothing the score function, leading to interpolated data.
problem Improving creativity in diffusion models.
method Analyzing the effect of score smoothing on diffusion model dynamics.
result Score smoothing causes diffusion models to generate data that interpolate the training set.
Paper proposes a method to reduce hallucinations in diffusion models using Laplacian score sharpening.
problem Hallucinations in diffusion models create incoherent or unrealistic samples.
method Post-hoc adjustment to the score function during inference using Laplacian approximation.
result Significantly reduces the rate of hallucinated samples across various data types.
New method synthesizes data on curved spaces for better interpolation.
problem Synthesizing data on curved spaces for better interpolation.
method Riemannian Diffusion Schrödinger Bridge
result Generalizes Diffusion Schrödinger Bridge to curved spaces for better interpolation.
Develops diffusion samplers for target distributions with efficient score and density estimates.
problem Estimating scores and densities for time-varying distributions.
method Sequential Monte Carlo with diffusion paths and control variates.
result Effective samplers for time-varying distributions with theoretical guarantees and practical applications.
The paper improves interpolation in generative models by using specific base distributions.
problem Unexpected side effects in linear interpolations of normalizing flows.
method Enforces a specific manifold using Dirichlet and von Mises-Fisher base distributions.
result Superior performance in terms of bits per dimension, FID, and KID scores for interpolation.
Proposes CDTD, a diffusion model for mixed-type tabular data.
problem Adapting diffusion models to mixed-type tabular data.
method Score matching and score interpolation for continuous features, adaptive noise schedules for categorical features.
result Consistently outperforms state-of-the-art models in mixed-type tabular data.
CSI method learns conditional distributions by estimating flow equations.
problem Learning conditional distributions in generative models.
method Estimates probability flow equations to transport reference to target distribution.
result Derives explicit expressions for conditional drift and score functions.
Unified framework for robust, stable, and efficient density ratio estimation.
problem Density-chasm and support-chasm problems in density ratio estimation.
method Dequantified diffusion-Schrödinger bridge (D3RE) framework with DDBI and DSBI.
result Offers uniform approximation and bounded time scores in theory and empirical performance.
The study evaluates different parameter selection methods for Gaussian process interpolation.
problem Choosing optimal parameters for Gaussian process interpolation.
method Empirical study using scoring rules and leave-one-out selection criteria.
result The choice of model family is often more important than the selection criterion.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
The article improves GP interpolation calibration using conformal prediction.
problem GP interpolation often produces poorly calibrated prediction intervals.
method Integrates conformal prediction with Gaussian process models.
result CP methods enhance prediction interval calibration without sacrificing accuracy.
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
A new loss function ED simplifies training energy-based models without scores.
problem Training energy-based models is computationally expensive.
method Energy Discrepancy (ED) loss function that does not rely on scores or MCMC.
result ED effectively interpolates between score matching and negative log-likelihood.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
A fundamental task in kernel methods is to pick nodes and weights, so as to approximate a given function from an RKHS by the weighted sum of kernel translates located at the nodes. This is the crux of kernel density estimation, kernel quadrature, or interpolation from discrete samples. Furthermore, RKHSs offer a conven…
RNGI model bridges two probability densities on Riemannian manifolds efficiently.
problem Limited applicability of Euclidean stochastic interpolants to Riemannian manifolds.
method Introduces RNGI model interpolating between Riemannian manifold probability densities along geodesics.
result Proves temporal marginal density solves transport equation on Riemannian manifold.
Proposes a new method for sampling from unknown distributions.
problem Challenges in sampling from distributions without direct sampling.
method Uses a dilation path to estimate score vectors in closed-form, guiding Langevin dynamics.
result Demonstrates improved sampling performance compared to classical methods.
Proposes a new method for feature selection using Bayesian ID with intervention.
problem Feature selection in data with varying importance.
method Probabilistic model for interpolative decomposition with Bayesian inference and Gibbs sampling.
result The proposed Bayesian ID algorithm with intervention selects features with higher priority and comparable reconstructive errors.
A new method for estimating density ratios in high dimensions.
problem Difficulty in accurately comparing probability distributions in high-dimensional settings.
method Divide-and-conquer approach via an infinite continuum of bridge distributions and time score matching.
result The proposed method effectively estimates density ratios and performs well on complex datasets.
Exact posterior score estimation for solving linear inverse problems
problem Solving linear inverse problems
method Derive the exact posterior score and use it as a denoising training objective
result EPS outperforms training-free and training-based baselines on various metrics
A new method for normalizing flows using stochastic interpolants simplifies likelihood estimation and improves efficiency.
problem Efficient and scalable likelihood estimation for complex probability distributions.
method Inference of velocity field from time-dependent density interpolating between base and target densities.
result Simplified quadratic loss for velocity estimation, leading to faster and more efficient training.
CSDI improves time series imputation by 40-65% over existing methods.
problem Imputing missing values in time series data.
method Conditional Score-based Diffusion models conditioned on observed data.
result CSDI improves by 40-65% over existing probabilistic imputation methods on popular metrics.
Paper accelerates diffusion models without retraining, reducing evaluations.
problem Approximating target data distributions efficiently.
method Training-free sampling algorithm using high-order Lagrange interpolation.
result Requires fewer score function evaluations than previous methods.
New conformal prediction methods for long-tailed classification problems.
problem Rare classes are systematically omitted in existing conformal prediction methods.
method Introduced a new conformal score function and a new interpolation procedure.
result Smoothly trade off set size and class-conditional coverage.
Proposes GMOTE for better handling imbalanced data.
problem Classification of imbalanced data.
method Generates minority class instances using Gaussian Mixture Model, considering outliers through Mahalanobis distance.
result Shows better accuracy and F1-Score when combined with CART or SVM.
This paper optimizes diffusion schedules for better sampling from data distributions.
problem Choosing an optimal discretization schedule for denoising diffusion models.
method Adaptive algorithm that selects an optimal schedule based on a work cost measure.
result The learned schedule recovers and outperforms manually tuned schedules.
This paper provides a practical method to extract caplet volatilities from quoted data.
problem Extracting caplet volatilities from quoted data is complex and not straightforward.
method The paper presents a constructive algorithm based on criteria and robust outlier detection. It includes direct interpolation, bootstrap methods, and global search methods.
result The paper introduces methods to extract caplet volatilities that are arbitrage-free and consistent with quoted data.
FUSE neural centrality framework improves data point measurement in high dimensions.
problem Measuring centrality in high-dimensional data is expensive and unstable.
method Combines global and local heads trained on arbitrary representations.
result Reveals meaningful classical ordering and competitive performance.
A new method improves density ratio estimation with fewer function evaluations.
problem Stable and accurate estimation of density ratios with high variance issues.
method Diffusion Secant Alignment for Score-Based Density Ratio Estimation (ISA-DRE)
result ISA-DRE achieves comparable or superior results with fewer function evaluations.
Training-free model learns SDE dynamics without training, accelerating parameter studies.
problem High computational cost of simulating parameter-dependent SDEs.
method Training-free conditional diffusion model with joint kernel-weighted Monte Carlo estimator.
result Accurate approximation of conditional distributions across varying parameter values.
New MCMC method improves sampling from multimodal distributions.
problem Sampling from multimodal distributions is challenging for classical MCMC methods.
method Interpolating along the diffusion path, preserving mode weights and mixing properties.
result MAD-Path sampler improves global exploration and mode-weight estimation.
AIS uses a suboptimal extended target distribution, which this paper improves using SGM.
problem Improving the efficiency of Annealed Importance Sampling for marginal likelihood estimation.
method Leveraging score-based generative modeling to approximate the optimal extended target distribution.
result Demonstrated novel, differentiable AIS procedures on synthetic and real-world data.
This paper provides guarantees for DFM models using KL divergence.
problem Ensuring generative models match target distributions efficiently.
method Using KL divergence and Brownian motion bridge for generative models.
result Non-asymptotic guarantees for DFM models under specific conditions.
The debate of what quantitative risk measure to choose in practice has mainly focused on the dichotomy between Value at Risk (VaR) -- a quantile -- and Expected Shortfall (ES) -- a tail expectation. Range Value at Risk (RVaR) is a natural interpolation between these two prominent risk measures, which constitutes a trad…
Bayesian method improves clinical trial efficiency.
problem Increase treatment effect estimates in clinical trials.
method Combines prognostic covariate adjustment with a Bayesian framework.
result Substantial increase in statistical power with controlled type I error.
This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.
problem The challenge of choosing between different interpolation methods for yield curve construction.
method Demonstrates the equivalence between forward rate interpolations and discount factor interpolations.
result Some popular interpolation methods on forward rates are equivalent to classical interpolation methods on discount factors.
The recent success of raw audio waveform synthesis models like WaveNet motivates a new approach for music synthesis, in which the entire process --- creating audio samples from a score and instrument information --- is modeled using generative neural networks. This paper describes a neural music synthesis model with fl…
Case vs control comparisons have been the classical approach to the study of neurological diseases. However, most patients will not fall cleanly into either group. Instead, clinicians will typically find patients that cannot be classified as having clearly progressed into the disease state. For those subjects, very lit…
Two methods improve Gaussian process predictive distributions' calibration.
problem Improving the reliability of Gaussian process predictive intervals.
method Introduces two methods: cps-gp and bcr-gp, both adapting conformal predictive systems to GP interpolation.
result Both methods provide finite-sample marginal calibration and smooth predictive distributions.
New FX option interpolations impact implied volatilities.
problem Different interpolations of FX option quotes lead to varying implied volatilities.
method Analysis of various exact interpolations of broker quotes.
result Different interpolations result in different implied volatilities.
Kernel interpolation is inconsistent for norms with smoothness above a constant.
problem Inconsistency of kernel interpolation in reproducing kernel Hilbert spaces.
method Lower bounds for generalization error in Sobolev norms.
result Kernel interpolation is always inconsistent for norms with smoothness above a constant.
Bayesian interpolants explain neural network inferences concisely.
problem Understanding neural network inferences.
method Adapting Craig interpolants for neural networks.
result Produces precise, understandable explanations.
Near-interpolating models grow norms quickly, affecting generalization.
problem Understanding the trade-off between interpolation and generalization in near-interpolating models.
method Random matrix theory and eigendecay analysis of data covariance matrix.
result Near-interpolating models exhibit rapid norm growth and worse generalization trade-offs.
SKI speeds up Toeplitz Neural Networks by avoiding explicit decay bias and using frequency response.
problem Efficiently compute and update Toeplitz matrices in neural networks.
method Sparse plus low-rank decomposition, asymmetric SKI, frequency response modeling.
result Achieved significant speedup with minimal performance loss.
LOCA learns standardized data coordinates from measurements.
problem Learning invariant data coordinates from non-linearly deformed manifolds.
method LOCA, a LOcal Conformal Autoencoder, learns an isometric embedding.
result LOCA preserves geometric information while learning invariant coordinates.
Deep neural networks can interpolate any dataset in the overparametrized regime.
problem Interpolating any dataset with deep neural networks in the overparametrized regime.
method Proving universal approximations and interpolating any dataset with deep neural networks, considering specific conditions on activation functions.
result Interpolation of any dataset is possible in the overparametrized regime with deep neural networks.
Interpolation hurts robust generalization even without noise.
problem The challenge of robust generalization in the absence of noise.
method Avoiding interpolation through ridge regularization.
result Ridge regularization improves robust generalization.
Uniform convergence of interpolators proven for Gaussian data.
problem Interpolation learning in high-dimensional linear regression with Gaussian data.
method Generic uniform convergence guarantee in terms of Gaussian width.
result Consistency of interpolators for minimum-norm and near-minimal-norm cases.