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Found 26 papers, 2 papers with code
Fast, Distribution-free Predictive Inference for Neural Networks with Coverage Guarantees
This paper introduces a novel, computationally-efficient algorithm for predictive inference (PI) that requires no distributional assumptions on the data and can be computed faster than existing bootstrap-type methods for neural networks.
Lazy Estimation of Variable Importance for Large Neural Networks
Recently, there has been a proliferation of model-agnostic methods to measure variable importance (VI) that analyze the difference in predictive power between a full model trained on all variables and a reduced model that excludes the variable(s) of interest.
Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefits
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational advantage.
The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning
The Internet of Things (IoT) is on the verge of a major paradigm shift.
Improved Prediction and Network Estimation Using the Monotone Single Index Multi-variate Autoregressive Model
Network estimation from multi-variate point process or time series data is a problem of fundamental importance.
Prediction in the presence of response-dependent missing labels
In a variety of settings, limitations of sensing technologies or other sampling mechanisms result in missing labels, where the likelihood of a missing label in the training set is an unknown function of the data.
Stochastic Gradient Descent in Correlated Settings: A Study on Gaussian Processes
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational advantage.
A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration
Rate matching deterministic lower bound for tensor reconstruction, which demonstrates the optimality of HOOI, is also provided.
Context-dependent self-exciting point processes: models, methods, and risk bounds in high dimensions
High-dimensional autoregressive point processes model how current events trigger or inhibit future events, such as activity by one member of a social network can affect the future activity of his or her neighbors.
ISLET: Fast and Optimal Low-rank Tensor Regression via Importance Sketching
In this paper, we develop a novel procedure for low-rank tensor regression, namely \emph{\underline{I}mportance \underline{S}ketching \underline{L}ow-rank \underline{E}stimation for \underline{T}ensors} (ISLET).
Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach
The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs.
Estimating Network Structure from Incomplete Event Data
Multivariate Bernoulli autoregressive (BAR) processes model time series of events in which the likelihood of current events is determined by the times and locations of past events.
Graph-based regularization for regression problems with alignment and highly-correlated designs
This work considers a high-dimensional regression setting in which a graph governs both correlations among the covariates and the similarity among regression coefficients -- meaning there is \emph{alignment} between the covariates and regression coefficients.
Network Estimation from Point Process Data
Using our general framework, we provide a number of novel theoretical guarantees for high-dimensional self-exciting point processes that reflect the role played by the underlying network structure and long-term memory.
Non-parametric Sparse Additive Auto-regressive Network Models
Using a combination of $\beta$ and $\phi$-mixing properties of Markov chains and empirical process techniques for reproducing kernel Hilbert spaces (RKHSs), we provide upper bounds on mean-squared error in terms of the sparsity $s$, logarithm of the dimension $\log d$, number of time points $T$, and the smoothness of the RKHSs.
Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)
We prove that this class of QVF DAG models is identifiable, and introduce a new algorithm, the OverDispersion Scoring (ODS) algorithm, for learning large-scale QVF DAG models.
Non-Convex Projected Gradient Descent for Generalized Low-Rank Tensor Regression
The two main differences between the convex and non-convex approach are: (i) from a computational perspective whether the non-convex projection operator is computable and whether the projection has desirable contraction properties and (ii) from a statistical upper bound perspective, the non-convex approach has a superior rate for a number of examples.
Inference of High-dimensional Autoregressive Generalized Linear Models
For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution.
Identifiability Assumptions and Algorithm for Directed Graphical Models with Feedback
Our simulation study supports our theoretical results, showing that the algorithms based on our two new principles generally out-perform algorithms based on the faithfulness assumption in terms of selecting the true skeleton for DCG models.
Learning Large-Scale Poisson DAG Models based on OverDispersion Scoring
In this paper, we address the question of identifiability and learning algorithms for large-scale Poisson Directed Acyclic Graphical (DAG) models.
Statistical and Algorithmic Perspectives on Randomized Sketching for Ordinary Least-Squares -- ICML
We then consider the statistical prediction efficiency (PE) and the statistical residual efficiency (RE) of the sketched LS estimator; and we use our framework to provide upper bounds for several types of random projection and random sampling algorithms.
A Statistical Perspective on Randomized Sketching for Ordinary Least-Squares
Prior results show that, when using sketching matrices such as random projections and leverage-score sampling algorithms, with $p < r \ll n$, the WC error is the same as solving the original problem, up to a small constant.
The Information Geometry of Mirror Descent
Using this equivalence, it follows that (1) mirror descent is the steepest descent direction along the Riemannian manifold of the exponential family; (2) mirror descent with log-likelihood loss applied to parameter estimation in exponential families asymptotically achieves the classical Cram\'er-Rao lower bound and (3) natural gradient descent for manifolds corresponding to exponential families can be implemented as a first-order method through mirror descent.
Learning directed acyclic graphs based on sparsest permutations
However, there is only limited work on consistency guarantees for score-based and hybrid algorithms and it has been unclear whether consistency guarantees can be proven under weaker conditions than the faithfulness assumption.
Early stopping and non-parametric regression: An optimal data-dependent stopping rule
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm.
Lower bounds on minimax rates for nonparametric regression with additive sparsity and smoothness
components from some distribution $\mP$, we determine tight lower bounds on the minimax rate for estimating the regression function with respect to squared $\LTP$ error.
