Research on mixed polynomials, extending non-degeneracy concepts to complex variables.
problem Extending non-degeneracy concepts to mixed polynomials in complex variables.
method Generalization of Mondal's partial non-degeneracy to mixed polynomials, introducing new concepts and proving properties.
result Strong partial non-degeneracy implies isolated singularities, and mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition.
Paper analyzes distributed learning with non-i.i.d. samples.
problem Learning rate analysis for distributed kernel ridge regression with dependent samples.
method Integral operator approach and covariance inequality for strong mixing sequences.
result Derives optimal learning rates for distributed kernel ridge regression.
New method for robust matrix completion with mixed data types.
problem Recovering a structured low rank matrix with mixed data types.
method Proposes a computationally feasible statistical approach with strong recovery guarantees for mixed data types.
result Strong recovery guarantees for low rank matrix completion with mixed data types.
The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using Φ-divergence.
problem Analyzing convergence rates of Langevin dynamics and Proximal Sampler.
method Extending mixing time analyses to Φ-divergence, using strong data processing inequalities. result Convergence of Φ-divergence to 0 exponentially fast along Unadjusted Langevin Algorithm and Proximal Sampler. Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that…
Superpixel-mix enhances reliability in semantic segmentation.
problem Improving reliability in real-world semantic segmentation.
method Superpixel-mix, a new data augmentation method with teacher-student consistency training.
result Superpixel-mix achieves state-of-the-art results in semi-supervised semantic segmentation.
Recent character and phoneme-based parametric TTS systems using deep learning have shown strong performance in natural speech generation. However, the choice between character or phoneme input can create serious limitations for practical deployment, as direct control of pronunciation is crucial in certain cases. We dem…
Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
problem Improving the mixing time of Gibbs sampler under strong log-concavity.
method Analyzing Gibbs sampler contraction under strong log-concavity, providing sharp contraction rate.
result Gibbs sampler contracts entropy linearly with condition number and independent of dimension under strong log-concavity.
SelectMix improves deep learning robustness against noisy labels.
problem Deep neural networks memorize noisy labels, degrading performance.
method Confidence-guided targeted sample mixing with soft labels.
result SelectMix consistently outperforms baseline methods on noisy label datasets.
We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants of 4-dimensional mapping tori in terms of Lefschetz numbers on HF+.
We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contracti…
New method combines domain changes and sparse mixing for better latent variable learning.
problem Challenges in identifying latent variables due to insufficient domain changes and violated sparsity constraints.
method Combines sufficient changes and sparse mixing constraints, using domain encoding networks and variational autoencoders.
result Identifiability of latent variables achieved with less restrictive constraints.
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive model…
The paper extends geometric results from negatively-curved spaces to strictly convex Hilbert geometry.
problem Extending geometric results from negatively-curved spaces to strictly convex Hilbert geometry.
method Demonstrates dynamical and counting results for geometrically-finite strictly convex projective structures with Hilbert metric.
result Hilbert geodesic flow is strongly mixing and orbits and primitive closed geodesics equidistribute.
This paper compares methods for handling mixed-attribute data in GFMM neural networks.
problem Handling datasets with mixed features in GFMM neural networks.
method Three main methods: encoding, combining with other classifiers, and specific learning algorithms.
result Encoding methods and combining with decision trees improve GFMM models' performance.
Study nearest-neighbor radii under dependent sampling, finding they remain informative.
problem Analyzing nearest-neighbor radii under dependent sampling.
method Consider strong mixing dependent observations, establish distribution-free almost sure convergence and sharp non-asymptotic moment bounds.
result Nearest-neighbor geometry remains informative under dependence sampling.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
Paper introduces methods to create fair and accurate regression models.
problem Creating fair and accurate regression models.
method Mixed-integer optimization methods, exact formulations, branch-and-bound algorithm, coordinate descent algorithm.
result Developed methods produce fair and accurate models with reduced training times.
Lower bound on BART's mixing time increases with data points.
problem Slow mixing time in BART's MCMC chains.
method Simplified BART with a single tree and reduced MCMC moves.
result Mixing time grows exponentially with data points.
Forré introduces a new conditional independence notion for mixed variables.
problem Unified framework for random and non-stochastic variables.
method Unified framework of transitional conditional independence and causal calculus for iDMGs.
result Unified framework connects conditional independencies to graphical separation criteria.
We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …
Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.
problem Finding Nash equilibria in two-player zero-sum continuous games, especially in high dimensions.
method Parametrizing mixed strategies as mixtures of particles, updating their positions and weights using gradient descent-ascent.
result Global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic.
We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or make strong assumptions about the form of the mixing matrix. Our algorithm does…
Contrastive learning estimates transition kernels for continuous-time stochastic processes.
problem Estimating transition kernels for continuous-time stochastic processes without labeled data.
method Contrastive learning applied to strong-mixing continuous-time stochastic processes.
result Contrastive learning can estimate transition kernels for small-to-mid-range intervals in the diffusion case.
New method identifies causal relationships from interventions in complex systems.
problem Learning causal representations from unknown, latent interventions with general nonlinear mixing.
method Strong identifiability results with unknown single-node interventions, using geometric structure of transformed data.
result First instance of causal identifiability from non-paired interventions for deep neural network embeddings.
Study compares clustering methods for mixed-type data.
problem Challenges in clustering mixed-type data.
method Distance-based (k-prototypes, PDQ, convex k-means), probabilistic (KAY-means, MBNs, LCM).
result KAMILA, LCM, and k-prototypes perform best.
LSTM models improve macroeconomic forecasting with mixed frequency data.
problem Improving accuracy of macroeconomic forecasts using mixed frequency data.
method Adapted LSTM model to mixed frequency data, using U-MIDAS scheme.
result Proposed LSTM models outperform conventional MIDAS models in out-of-sample predictive performance.
We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results ar…
Stochastic Gradient Langevin Dynamics (SGLD) is a sampling scheme for Bayesian modeling adapted to large datasets and models. SGLD relies on the injection of Gaussian Noise at each step of a Stochastic Gradient Descent (SGD) update. In this scheme, every component in the noise vector is independent and has the same sca…
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories, achieving optimal performance.
problem Learning Gaussian graphical models from a single trajectory of a dependent stochastic process.
method Two algorithms based on dueling-neighborhood search and local statistics built from the update sequence of Glauber dynamics.
result Achieve κ−2 dependence of the information-theoretic lower bounds, mixing-free and signal-optimal. The paper tackles deep learning from dependent data, achieving optimal performance.
problem Deep learning from strongly mixing observations, especially with regularization and optimality.
method Sparse-penalized regularization for deep neural networks, oracle inequality for expected excess risk.
result Deep neural network estimator achieves minimax optimal rate for nonparametric autoregression.
Uniform counting formulas for orthogeodesics in Kleinian groups converge.
problem Counting orthogeodesics in Kleinian groups converging to a limit.
method Spectral gap of the limit manifold and geodesic flow mixing property.
result Asymptotically uniform counting formulas for orthogeodesics.
Proposes a new model for context-dependent decision-making.
problem Constant preference parameters in decision models are too rigid.
method Introduces Context-aware Bayesian mixed multinomial logit model using neural networks.
result Models context-dependent intra-respondent heterogeneity effectively.
Separating mixed distributions is a long standing challenge for machine learning and signal processing. Most current methods either rely on making strong assumptions on the source distributions or rely on having training samples of each source in the mixture. In this work, we introduce a new method---Neural Egg Separat…
We study a stochastic equation modeling the lay-down of fibers in the production process of nonwovens. The equation can be formulated as some manifold-valued Stratonovich stochastic differential equation. Especially, we study the long time behaviour of the stochastic process. Demanding mathematical difficulties arising…
Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing materi…
A DP method selects best sparse models in high dimensions efficiently.
problem Model selection in high-dimensional sparse linear regression under privacy constraints.
method Differential privacy (DP) with exponential mechanism and Metropolis-Hastings algorithm.
result The method identifies active features quickly under privacy constraints.
Develops conformal Bayes for two-sided censored Gaussian regression under label shift.
problem Prediction under label shift with censored responses.
method Combines posterior predictive tilting with weighted conformal calibration.
result Restores marginal coverage with smaller prediction sets.
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, nam…
The study introduces a holdout-based framework to assess synthetic data fidelity and privacy.
problem Evaluating the quality and privacy of synthetic data solutions for mixed-type tabular data.
method Holdout-based empirical assessment framework measuring fidelity and privacy risk.
result Synthetic data samples are as close to the training as to the holdout data, indicating generalization and independence from individual records.
In mixed multi-view data, multiple sets of diverse features are measured on the same set of samples. By integrating all available data sources, we seek to discover common group structure among the samples that may be hidden in individualistic cluster analyses of a single data-view. While several techniques for such int…
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
Paper tackles offline RL from mixed datasets with adaptive KL regularizer.
problem Challenges in optimizing RL and BC signals with varying action coverage and multiple action modes.
method Adaptively weighted reverse KL divergence regularizer based on TD3 algorithm.
result Empirically outperforms existing offline RL algorithms in MuJoCo locomotion tasks.
Split conformal prediction works well for time series despite temporal dependence.
problem Uncertainty quantification for time series predictions with past data.
method Split conformal prediction method for time series data with predictors having memory.
result Theoretical bounds on coverage probability for split conformal prediction in time series with memory.
2D-PT improves sampling in constrained optimization problems.
problem Sampling Boltzmann distributions with soft constraints.
method Two-dimensional extension of parallel tempering.
result 2D-PT achieves near-ideal mixing in constrained problems.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how p…
A new perspective on self-attention models using MLPs.
problem Improving sequence modeling with self-attention mechanisms.
method Introducing HyperMLP and HyperGLU, which use dynamic two-layer MLPs with reverse-offset layout.
result HyperMLP/HyperGLU consistently outperform softmax-attention baselines.