arXiv research

Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.

Deep-HGP uses Bayesian nonparametric approach for complex data regression.

Deep model tackles claim size modeling with quantile-based regression.

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\log n$-factors) under a general composition assumption on the re…

DSPPs improve predictive distributions in scalable regression tasks.

HKRR adapts to MIM, overcoming the curse of dimensionality.

Paper proposes deep neural networks for nonparametric regression from dependent data.

Materials discovery is crucial for making scientific advances in many domains. Collections of data from experiments and first-principle computations have spurred interest in applying machine learning methods to create predictive models capable of mapping from composition and crystal structures to materials properties. …

Deep single-index Fréchet regression for metric space-valued outputs

The paper tackles deep learning from dependent data, achieving optimal performance.

Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.

Conditional DGP learns effective kernels from low-fidelity data.

Study on deep neural networks using branching processes and Mehler's formula.

Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…

This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.

Develops a deep learning framework for various data types.

DFNNs predict non-Euclidean responses from Euclidean predictors.

Deep networks learn sparse hierarchical features without CoD.

Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with explicit and implicit regularizations. Our claims are being established with several im…

A novel model uses ODE-based random features to model nonlinear dynamical systems.

Unified analysis of multi-task functional linear regression with manifold and composite penalties.

Paper introduces arctan pinball loss for XGBoost quantile regression.

New methods for predicting compositional data using conformal prediction.

We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and the Lipschitz constant decreases inversely with the number $m$ of functions com…

This paper examines how noise affects deep neural networks and improves their performance.

Deep neural networks are optimal for dependent data using PAC-Bayes bounds.

Paper tackles distributed linear regression with compositional covariates.

Paper simplifies DP composition for adaptive privacy budgets, enabling better privacy and accuracy in deep learning.

Deep learning can learn compositional functions more efficiently by breaking them into stages.

New ANN method for imputing rounded zeros in compositional data.

New framework interprets deep neural networks through input structure.

Standard methods in deep learning for natural language processing fail to capture the compositional structure of human language that allows for systematic generalization outside of the training distribution. However, human learners readily generalize in this way, e.g. by applying known grammatical rules to novel words.…

Adapts Altman's model to compositional data for bankruptcy prediction.

Recent findings in multi-agent deep learning systems point towards the emergence of compositional languages. These claims are often made without exact analysis or testing of the language. In this work, we analyze the emergent language resulting from two different cooperative multi-agent game with more exact measures fo…

Sharp privacy bounds for sequential analysis of sensitive data.

Smooth DNNs mitigate the curse of dimensionality in uniform convergence for various regression tasks.

Develops methods for causal inference in compositional data using instrumental variables.

Sublinearly structured DNNs achieve feature learning consistency for compositional functions.

Deep learning enhances art market valuation by incorporating visual data.

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrtκ)$ and thus achieves the optimal …

CTLNet predicts Shanghai Composite Index with improved accuracy.

We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it leads to a convergence rate of O(1/n) without strong convexity assumptions. This …

We propose novel deep learning based chemometric data analysis technique. We trained L2 regularized sparse autoencoder end-to-end for reducing the size of the feature vector to handle the classic problem of the curse of dimensionality in chemometric data analysis. We introduce a novel technique of automatic selection o…

FFN addresses spectral bias in neural value approximation, improving reinforcement learning performance.

Proposes PENNs for deep learning with missing data.

Deep neural networks can approximate complex functions through repeated compositions of a fixed-size ReLU network.

Novel framework predicts brain biomarker trajectories with superior performance.

New method for causal inference with complex treatment compositions.