This paper extends ABCD to discover time series structure using probabilistic program synthesis.
problem Discovering structure in time series data.
method Formulating ABCD in probabilistic program synthesis, using abstract syntax trees and probabilistic programs.
result Improved accuracy in time series clustering and interpolation/extrapolation.
Curvature tensors can always be matched to a metric tensor under certain conditions.
problem Sectionally positive curvature tensors and their relationship to metric tensors.
method Existence and uniqueness of a metric tensor gab such that Rabcdgbd=gacλ. result A metric tensor gab can be found for sectionally positive curvature tensors, and it is unique up to a constant factor. The paper studies the face angles of tetrahedra with a fixed base.
problem Determine the closure and boundary of the set of face angles of tetrahedra with a given base.
method Analyzes the set of tetrahedra with a given base and calculates the cosine of the angles between the faces.
result The closure and boundary of the set of face angles are determined.
ABCD model generates synthetic graphs for community detection with improved scalability and interpretability.
problem Synthetic graphs for community detection are limited in scalability and interpretability.
method Developed a new random graph model (ABCD) with community structure and power-law distribution.
result ABCD model solves scalability and interpretability issues of LFR model.
We prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kaehler metric on a compact Hermitian symmetric spaces of ABCD--type.
Neural network predicts intelligence from brain structure measurements.
problem Predicting intelligence scores from brain structure measurements.
method Four-layer fully-connected neural network (FNN) using volumes, WM/GM contrast, and cortical thickness.
result Achieved MSE of 94.0270 in test set.
Develops a new method to analyze brain networks for cognitive traits.
problem Challenges in summarizing and relating brain connectomes to human traits.
method Graph Auto-Encoding (GATE) model using deep learning.
result GATE improves prediction accuracy and efficiency over existing methods.
Bayesian Deep Noise Neural Network (B-DeepNoise) estimates predictive densities and uncertainty.
problem Estimating predictive densities and uncertainty in deep neural networks.
method Extends random noise to all hidden layers, using Gibbs sampling for posterior computation.
result Superior performance in prediction accuracy and uncertainty quantification.
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and examples are provided. This continues the investigation begun in [ABCDS] where the met…
The paper introduces invariants to describe period-doubling routes to chaos in dynamical systems.
problem Understanding the dynamics of period-doubling routes to chaos in complex systems.
method Introducing three topological invariants to describe the topology of period-doubling routes to chaos.
result Ascribed symbolic dynamics to perturbations of the Shilnikov homoclinic scenario and dynamics of the Henon map.
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with …
Proposes smoothing input and weight spaces for semi-supervised learning.
problem Improving semi-supervised learning performance with minimal data augmentation.
method Combines input-space and weight-space smoothing through adversarial optimization.
result Achieves comparable performance to state-of-the-art without heavy data augmentation.
PIML model improves hydrological predictions by blending physics and ML.
problem Hydrological models either lack predictive accuracy or fail to maintain physical consistency.
method Physics Informed Machine Learning (PIML) that integrates physics-based models and ML algorithms.
result PIML model outperforms both physics-based and ML models in predicting streamflow and evapotranspiration.
Selective inference improves multi-task neuroimaging analysis.
problem Improving predictive performance and modeling accuracy in neuroimaging studies.
method Proposes a framework for selective inference to jointly identify relevant covariates and conduct valid inference in a sparsity-inducing model.
result Selective inference yields tighter confidence intervals and more accurate signal recovery than single-task methods.