Related papers: Inference on High-dimensional Single-index Models …
We investigate boosted online regression and propose a novel family of regression algorithms with strong theoretical bounds. In addition, we implement several variants of the proposed generic algorithm. We specifically provide theoretical…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
Single-index models are a class of functions given by an unknown univariate ``link'' function applied to an unknown one-dimensional projection of the input. These models are particularly relevant in high dimension, when the data might…
Projection-based model reduction enables efficient simulation of complex dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. The Operator Inference (OpInf) approach learns such reduced surrogate…
Let $(Y_t)_{t\geq 1}$ be a sequence of i.i.d.\ observations and $\{f_\theta,\theta\in \mathbb{R}^d\}$ be a parametric model. We introduce a new online algorithm for computing a sequence $(\hat{\theta}_t)_{t\geq 1}$ which is shown to…
Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that…
Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network…
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…
Inferring the connectivity structure of networked systems from data is an extremely important task in many areas of science. Most of real-world networks exhibit sparsely connected topologies, with links between nodes that in some cases may…
In the common partially linear single-index model we establish a Bahadur representation for a smoothing spline estimator of all model parameters and use this result to prove the joint weak convergence of the estimator of the index link…
Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some…
Intelligent real-world systems critically depend on expressive information about their system state and changing operation conditions, e.g., due to variation in temperature, location, wear, or aging. To provide this information, online…
Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model…
Hierarchical inference systems route tasks across multiple computational layers, where each node may either finalize a prediction locally or offload the task to a node in the next layer for further processing. Learning optimal routing…
The state-of-the-art online learning models generally conduct a single online gradient descent when a new sample arrives and thus suffer from suboptimal model weights. To this end, we introduce an online broad learning system framework with…
Streaming data often exhibit heterogeneity due to heteroscedastic variances or inhomogeneous covariate effects. Online renewable quantile and expectile regression methods provide valuable tools for detecting such heteroscedasticity by…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…