A Survey of Tuning Parameter Selection for High-Dimensional Regression

Wu, Yunan; Wang, Lan

doi:10.1146/annurev-statistics-030718-105038

Cited by 31 publications

(10 citation statements)

References 70 publications

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“…There still exits an important gap between the theory and practice of Lasso. See also Wu and Wang (2020) for a recent survey on tuning parameter selection for high-dimensional regression.…”

Section: Introductionmentioning

confidence: 99%

A Tuning-free Robust and Efficient Approach to High-dimensional Regression

Wang

Peng

Bradić

et al. 2020

Journal of the American Statistical Association

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We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintaining high efficiency for normal random errors. Comparing with other alternative robust regression procedures, it also enjoys the property of being equivariant when the response variable undergoes a scale transformation. Computationally, it can be efficiently solved via linear programming. Theoretically, under weak conditions on the random error distribution, we establish a finite-sample error bound with a near-oracle rate for the new estimator with the simulated tuning parameter. Our results make useful contributions to mending the gap between the practice and theory of Lasso and its variants. We also prove that further improvement in efficiency can be achieved by a second-stage enhancement with some light tuning. Our simulation results demonstrate that the proposed methods often outperform cross-validated Lasso in various settings. Supplementary materials for this article are available online.

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“…There still exits an important gap between the theory and practice of Lasso. See also Wu and Wang (2020) for a recent survey on tuning parameter selection for high-dimensional regression.…”

Section: Introductionmentioning

confidence: 99%

A Tuning-free Robust and Efficient Approach to High-dimensional Regression

Wang

Peng

Bradić

et al. 2020

Journal of the American Statistical Association

Self Cite

View full text Add to dashboard Cite

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“…from data splitting) into the portfolio construction. One can also find a similar discussion in a survey on tuning parameter selection for regression models in [61]. In the context of regression, [55] shows that CV is asymptotically equivalent to the Akaike's information criterion (AIC).…”

mentioning

confidence: 76%

A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection

Pun¹

2021

SIAM J. Finan. Math.

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This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of relative-volatility-managed portfolio (RVMP). The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio's risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross-validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE portfolio, which beats the equally-weighted portfolio and improves over the shrinkage portfolio.

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“…One of the core challenges in high-dimensional penalized regression is determining a suitable regularization parameter λ that trades off sparsity (i.e., interpretability) of the model coefficients and out-of-sample predictive 5/21 performance of the model [66,67]. Standard procedures for (hierarchical) interaction models include cross-validation [53] and Information Criteria, including the Aikake (AIC) and the extended Bayesian Information Criterion (BIC) [55].…”

Section: Stability-based Model Selection For Hierarchical Interactionsmentioning

confidence: 99%

asteRIa enables robust interaction modeling between chromatin modifications and epigenetic readers

Stadler,

Lukauskas,

Bartke

et al. 2024

Preprint

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Chromatin, the nucleoprotein complex consisting of DNA and histone proteins, plays a crucial role in regulating gene expression by controlling access to DNA. Chromatin modifications are key players in this regulation, as they help to orchestrate DNA transcription, replication, and repair. These modifications recruit epigenetic "reader" proteins, which mediate downstream events. Most modifications occur in distinctive combinations within a nucleosome, suggesting that epigenetic information can be encoded in combinatorial chromatin modifications. A detailed understanding of how multiple modifications cooperate in recruiting such proteins has, however, remained largely elusive. Here, we integrate nucleosome affinity purification data with high-throughput quantitative proteomics and hierarchical interaction modeling to estimate combinatorial effects of chromatin modifications on protein recruitment. This is facilitated by the computational workflow asteRIa which combines hierarchical interaction modeling, stability-based model selection, and replicate-consistency checks for a stable estimation of Robust Interactions among chromatin modifications. asteRIa identifies several epigenetic reader candidates responding to specific interactions between chromatin modifications. For the polycomb protein CBX8, we independently validate our results using genome-wide ChIP-Seq and bisulphite datasets. We provide the first quantitative framework for identifying cooperative effects of chromatin modifications on protein binding.

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A Survey of Tuning Parameter Selection for High-Dimensional Regression

Cited by 31 publications

References 70 publications

A Tuning-free Robust and Efficient Approach to High-dimensional Regression

A Tuning-free Robust and Efficient Approach to High-dimensional Regression

A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection

asteRIa enables robust interaction modeling between chromatin modifications and epigenetic readers

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