Optimal Biweight kernel and computationally efficient Epanechnikov kernel for modal linear regression.
problem Finding the best kernel for modal linear regression.
method Refined analysis of asymptotic statistical behavior and IRLS algorithm convergence.
result Biweight kernel minimizes asymptotic mean squared error, Epanechnikov kernel guarantees IRLS convergence.
Proposes MVGPR for spatiotemporal data modal analysis.
problem Sparse and irregularly sampled data in complex flows.
method Multivariate Gaussian process regression (MVGPR) with kernel design.
result MVGPR outperforms DMD and SPOD in modal analysis of sparse and irregular data.
This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially moda…
Wasserstein framework solves mixed linear regression problems.
problem Mixed linear regression with multi-modal distributions.
method Wasserstein distance minimization for nonconvex-concave minimax optimization.
result WMLR achieves global convergence and generalization guarantees for two linear models.
Proposes a parametric modal regression method using the implicit function theorem.
problem Finding conditional modes for multi-modal conditional distributions.
method Uses the implicit function theorem to develop an objective function for learning a joint function over inputs and targets.
result Empirically demonstrates scalability and effectiveness in learning multi-valued functions and high-dimensional inputs.
TAP transfers knowledge from unlabeled data to improve cross-modal learning.
problem Improving supervised learning performance using unlabeled data from a different modality.
method Probabilistic approach for missing information estimation, kernel regression, cross-attention module, TAP neural network.
result TAP significantly improves generalization across different domains and neural network architectures.
Modal regression estimates the local modes of the distribution of Y given X=x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of …
Bayesian method selects important covariates in modal regression.
problem Bayesian modal regression with heavy-tailed responses.
method Expectation-maximization algorithm for parameter estimation; test statistic for variable selection.
result Efficacy of the proposed method in identifying important covariates.
This paper analyzes RMR under Markov-dependent samples, improving understanding of its generalization error.
problem Understanding the generalization error of RMR in Markov-dependent settings.
method Established the upper bound for RMR estimator under Markov-dependent samples, providing a learning rate.
result Markov dependence affects the generalization error, reducing it by a multiplicative factor of the spectral gap.
InVA models image outcomes from multiple modalities, outperforming standard VAEs.
problem Understanding relationships across multiple imaging modalities in neuroimaging.
method Integrative Variational Autoencoder (InVA) framework for image-on-image regression.
result InVA accurately predicts PET scans from structural MRI, outperforming conventional models.
Modal regression is aimed at estimating the global mode (i.e., global maximum) of the conditional density function of the output variable given input variables, and has led to regression methods robust against heavy-tailed or skewed noises. The conditional mode is often estimated through maximization of the modal regre…
Paper addresses high-dimensional linear regression with missing data, proposing efficient and nearly unbiased estimators.
problem High-dimensional linear regression with blockwise missing covariates and partially observed responses.
method Proposes a computationally efficient estimator and nearly unbiased debiased estimators using blockwise imputation and estimating equations.
result Asymptotically valid confidence intervals and statistical tests constructed based on debiased estimators.
This paper proposes MM-DAGs for analyzing traffic congestion, learning multiple DAGs jointly.
problem Analyzing multi-modal traffic data with overlapping and distinct variables.
method Developed MM-DAGs for multi-task, multi-modal DAG learning, using multi-modal regression and CD measure.
result Proved the effectiveness of MM-DAGs in traffic congestion analysis.
This work tackles uncertainty in multi-agent multi-modal trajectory forecasting.
problem Measuring and ranking uncertainty in multi-agent multi-modal trajectory forecasting.
method Proposes collaborative uncertainty (CU) and a CU-aware regression framework.
result The CU-aware regression framework improves SOTA systems' performances.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …
Recently, a number of statistical problems have found an unexpected solution by inspecting them through a "modal point of view". These include classical tasks such as clustering or regression. This has led to a renewed interest in estimation and inference for the mode. This paper offers an extensive survey of the tradi…
GEM learns a manifold for cross-modal data, capturing structure without modality dependence.
problem Modality-specific neural models limit flexibility and custom architecture.
method Casts learning as manifold inference, enforcing coverage, linearity, and isometry.
result GEM learns latent structure across image, shape, audio, and cross-modal domains.
Unified model learns joint and individual features from brain imaging data.
problem Integrating structural and functional connectivity data for behavioral phenotypes.
method Cross-Modal Joint-Individual Variational Network (CM-JIVNet) with multi-head attention fusion.
result CM-JIVNet outperforms in cross-modal reconstruction and behavioral trait prediction.
In this paper, we propose a novel method for projecting data from multiple modalities to a new subspace optimized for one-class classification. The proposed method iteratively transforms the data from the original feature space of each modality to a new common feature space along with finding a joint compact descriptio…
New method identifies shared components from unpaired multimodal mixtures.
problem Identify shared components from unpaired multimodal mixtures.
method Distribution divergence minimization-based loss with sufficient conditions for identifiability.
result Sufficient conditions for shared component identifiability from unaligned multimodal mixtures.
Enhances CLIP's similarity computation using PMI's linear structure.
problem CLIP's similarity computation misses the optimal linear structure of PMI.
method KME-CLIP, utilizing inner product in a reproducing kernel Hilbert space.
result KME-CLIP approximates PMI with arbitrary accuracy and outperforms CLIP.
The heterogeneity-gap between different modalities brings a significant challenge to multimedia information retrieval. Some studies formalize the cross-modal retrieval tasks as a ranking problem and learn a shared multi-modal embedding space to measure the cross-modality similarity. However, previous methods often esta…
Framework for reconstructing nonlinear systems from multi-modal time series data.
problem Reconstructing nonlinear dynamical systems from multi-modal time series data.
method Dynamic interpretable recurrent neural networks coupled with generalized linear models for multi-modal data integration.
result Framework efficiently compensates for noisy or missing information in one data channel using other channels.
New framework shows cross-attention improves multi-modal in-context learning.
problem Understanding multi-modal in-context learning in neural networks.
method Mathematical framework and linearized cross-attention mechanism.
result Cross-attention mechanism is provably optimal for multi-modal in-context learning.
Nash integrates covariate-specific side info into sparse regression via neural networks.
problem Sparse linear regression struggles with covariates exhibiting structure or coming from heterogeneous sources.
method Neural Adaptive Shrinkage (Nash) framework that integrates side information into sparse regression via neural networks. Uses split variational empirical Bayes algorithm.
result Nash improves accuracy and adaptability over existing methods in real data experiments.
We propose a tri-modal architecture to predict Big Five personality trait scores from video clips with different channels for audio, text, and video data. For each channel, stacked Convolutional Neural Networks are employed. The channels are fused both on decision-level and by concatenating their respective fully conne…
Integrates neural encoders into GLMMs for multimodal data analysis.
problem Scalable Bayesian inference for GLMMs assumes low-dimensional tabular predictors and does not handle high-dimensional modalities.
method Jointly learns modality-specific neural encoders with GLMM objective, performs variance-corrected stochastic-gradient MCMC.
result Preserves interpretable fixed and random effects while scaling to large longitudinal datasets.
Contrastive learning adapts to data intrinsic dimensions, learning low-dimensional representations.
problem Learning high-dimensional representations from multi-modal data.
method Multi-modal contrastive learning with temperature optimization.
result Contrastive learning adapts to intrinsic dimensions of data, not specified dimensions.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
Shifts dataset evaluates uncertainty in real-world tasks across modalities.
problem Lack of standard datasets for evaluating uncertainty estimation and robustness to distributional shift.
method Proposes Shifts Dataset for evaluation of uncertainty estimates and robustness to distributional shift across tabular, audio, text, and sensor data.
result Baseline results for tabular weather prediction, machine translation, and SDC vehicle motion prediction.
New method tackles tensor regression with robust Kaczmarz approach.
problem Reconstructing tensor signals from corrupted measurements.
method Quantile-based randomized Kaczmarz method for tensor linear systems.
result Improved convergence and robustness to adversarial corruptions.
Anomaly detection is a fundamental problem in data mining field with many real-world applications. A vast majority of existing anomaly detection methods predominately focused on data collected from a single source. In real-world applications, instances often have multiple types of features, such as images (ID photos, f…
Proposes ℓ0-CCA for sparse CCA with improved representation learning.
problem CCA models break with too many variables, and sparsity is beneficial.
method Sparse CCA with stochastic gates and ℓ0-regularization. result Improves representation learning by gating nuisance variables.
A Python package for GLHMM, a flexible HMM framework.
problem Handling diverse HMM applications in neuroscience.
method Stochastic variational inference for large datasets.
result Enables statistical testing and out-of-sample prediction.
T-EMDE bridges the heterogeneity gap between image and text modalities.
problem Finding similarities between image and text modalities with non-related feature spaces.
method Inspired by EMDE, T-EMDE uses sketches for multimodal operations, avoiding self-attention's quadratic complexity.
result T-EMDE achieves state-of-the-art results and reduces model latency.
Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to construct a consistent modal regression algorithm.
Graph convolution network based approaches have been recently used to model region-wise relationships in region-level prediction problems in urban computing. Each relationship represents a kind of spatial dependency, like region-wise distance or functional similarity. To incorporate multiple relationships into spatial …
GACEM optimizes complex multi-modal problems using neural networks.
problem Black-box optimization and constraint satisfaction in multi-modal environments.
method Modified Cross-Entropy Method with masked auto-regressive neural network.
result GACEM outperforms traditional CEM in diverse solutions, mode discovery, and sample efficiency.
This work improves manifold learning for multi-modal data.
problem Distortions and modeling errors in multi-modal data.
method Isometrizing learned Riemannian structure and balancing regularity and expressivity.
result The synergy of proposed approaches enhances manifold learning.
FBMS R package simplifies Bayesian model selection and averaging.
problem Complex regression settings with multi-modal posterior landscapes.
method Efficient MJMCMC and GMJMCMC algorithms for Bayesian model exploration.
result FBMS effectively handles Bayesian generalized linear and nonlinear models.
The paper reviews and extends calibration concepts for classification and regression.
problem Formalizing compatibility between probabilistic predictions and outcomes.
method Review and extension of existing calibration concepts, introduction of new concepts.
result Hierarchical relations between calibration concepts for various data types.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial …
Study predicts stock price direction on earnings announcement days using multi-modal deep learning.
problem Predicting stock price movements during earnings announcements is challenging due to market noise and discontinuities.
method Constructed a multi-modal feature space combining fundamental metrics, technical indicators, and sentiment scores from financial news articles. Evaluated LSTM and Transformer models against a baseline.
result Transformer model outperforms LSTM in identifying volatile movements, achieving higher macro F1-score.
Study on deep learning for speckle noise reduction in imaging modalities.
problem Multiplicative speckle noise challenges conventional deep learning methods for speckle denoising.
method Likelihood-based deep neural network (DNN) estimators for nonparametric regression under speckle noise.
result Established minimax rates for speckle denoising, matching those for additive Gaussian noise alone.
The paper introduces new estimators for multivariate functions using Fourier methods.
problem Estimating multivariate functions like densities and regression functions.
method Monte Carlo estimators based on the Fourier integral theorem.
result Established rates of convergence for new estimators, often superior to existing methods.
SBCA optimizes portfolios by fusing price data and text sentiment.
problem Insufficient integration of multi-modal information in traditional portfolio optimization models.
method Cross-modal BERT-driven Actor-Critic framework with gated fusion and constraint embedding.
result SBCA outperforms benchmarks in portfolio value, return, Sharpe ratio, and maximum drawdown.