Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTransfer Learning under High-dimensional Generalized Linear Models
102
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose an oracle algorithm and derive its $ell_2$-estimation error bounds. The theoretical analysis shows that under certain conditions, when the target and source are sufficiently close to each other, the estimation error bound could be improved over that of the classical penalized estimator using only target data. When we dont know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms.
rate research
Read More
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights, and the nonlinear function. While methods have been described to learn SIMs in the low dimensional regime, a method that can efficiently learn SIMs in high dimensions has not been forthcoming. We propose three variants of a computationally and statistically efficient algorithm for SIM inference in high dimensions. We establish excess risk bounds for the proposed algorithms and experimentally validate the advantages that our SIM learning methods provide relative to Generalized Linear Model (GLM) and low dimensional SIM based learning methods.
We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, for the average cost LQ problem, a regret bound of ${O}(sqrt{T})$ was shown, apart form logarithmic factors. However, this bound scales exponentially with $p$, the dimension of the state space. In this work we consider the case where the matrices describing the dynamic of the LQ system are sparse and their dimensions are large. We present an adaptive control scheme that achieves a regret bound of ${O}(p sqrt{T})$, apart from logarithmic factors. In particular, our algorithm has an average cost of $(1+eps)$ times the optimum cost after $T = polylog(p) O(1/eps^2)$. This is in comparison to previous work on the dense dynamics where the algorithm requires time that scales exponentially with dimension in order to achieve regret of $eps$ times the optimal cost. We believe that our result has prominent applications in the emerging area of computational advertising, in particular targeted online advertising and advertising in social networks.
Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Omega(n^{2/3})$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is smaller than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that $Theta(n^{2/3})$ is the optimal rate in the data-poor regime. The results complement existing bounds for the data-rich regime and provide another example where carefully balancing the trade-off between information and regret is necessary. Finally, we prove a dimension-free $O(sqrt{n})$ regret upper bound under an additional assumption on the magnitude of the signal for relevant features.
We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high dimensionality in the covariates can impose adverse impacts on the power of the test. We propose a test formation which can avoid the adverse impact of the high dimensionality. When the inverse of the link function is bounded such as the logistic or probit regression, the proposed test is as good as Goeman et al. (2011)s test. The proposed tests provide p-values for testing significance for gene-sets as demonstrated in a case study on an acute lymphoblastic leukemia dataset.
A number of universally consistent dependence measures have been recently proposed for testing independence, such as distance correlation, kernel correlation, multiscale graph correlation, etc. They provide a satisfactory solution for dependence testing in low-dimensions, but often exhibit decreasing power for high-dimensional data, a phenomenon that has been recognized but remains mostly unchartered. In this paper, we aim to better understand the high-dimensional testing scenarios and explore a procedure that is robust against increasing dimension. To that end, we propose the maximum marginal correlation method and characterize high-dimensional dependence structures via the notion of dependent dimensions. We prove that the maximum method can be valid and universally consistent for testing high-dimensional dependence under regularity conditions, and demonstrate when and how the maximum method may outperform other methods. The methodology can be implemented by most existing dependence measures, has a superior testing power in a variety of common high-dimensional settings, and is computationally efficient for big data analysis when using the distance correlation chi-square test.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
