A large covariance matrix estimator under intermediate spikiness regimes

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such un-shrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when $n$ is at least $O(p^{\frac{3}{2}\delta})$, provided that the maximum number of non-zeros per row in the sparse component is $O(p^{\delta})$ with $\delta \leq \frac{1}{2}$. Consistent recovery is ensured if the latent eigenvalues scale to $p^{\alpha}$, $\alpha \in[0,1]$, while rank consistency is ensured if $\delta \leq \alpha$. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data

The Importance of Being Clustered: Uncluttering the Trends of Statistics from 1970 to 2015

In this paper we retrace the recent history of statistics by analyzing all the papers published in five prestigious statistical journals since 1970, namely: Annals of Statistics, Biometrika, Journal of the American Statistical Association, Journal of the Royal Statistical Society, series B and Statistical Science. The aim is to construct a kind of "taxonomy" of the statistical papers by organizing and by clustering them in main themes. In this sense being identified in a cluster means being important enough to be uncluttered in the vast and interconnected world of the statistical research. Since the main statistical research topics naturally born, evolve or die during time, we will also develop a dynamic clustering strategy, where a group in a time period is allowed to migrate or to merge into different groups in the following one. Results show that statistics is a very dynamic and evolving science, stimulated by the rise of new research questions and types of data

High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization

We propose a new estimator of the regression coefficients for a high-dimensional linear regression model, which is de rived by replacing the sample predictor covariance matrix in the OLS estimator with a different predictor covariance matrix estimate obtained by a nuclear norm plus l1 norm penalization. We call the estimator ALCE-reg. We make a direct theoretical comparison of the expected mean square error of ALCE-reg with OLS and RIDGE. We show in a sim ulation study that ALCE-reg is particularly effective when both the dimension and the sample size are large, due to its ability to find a good compromise between the large bias of shrinkage estimators (like RIDGE and LASSO) and the large variance of estimators conditioned by the sample predictor covariance matrix (like OLS and POET)

Book of abstracts: Scientific Opening of The Microsoft Reasearch Centre for Computational and Systems Biology, Trento, Italy, April 3-5, 2006

Abstracts of the talks of the Scientific Opening of the Microsoft Research - University of Trento Centre for Computational and Systems Biology held in Trento on April 3-5, 200

Monocyte-macrophage differentiation of acute myeloid leukemia cell lines by small molecules identified through interrogation of the Connectivity Map database

The transcription factor C/EBPα is required for granulocytic differentiation of normal myeloid progenitors and is frequently inactivated in acute myeloid leukemia (AML) cells. Ectopic expression of C/EBPα in AML cells suppresses proliferation and induces differentiation suggesting that restoring C/EBPα expression/activity in AML cells could be therapeutically useful. Unfortunately, current approaches of gene or protein delivery in leukemic cells are unsatisfactory. However, "drug repurposing" is becoming a very attractive strategy to identify potential new uses for existing drugs. In this study, we assessed the biological effects of candidate C/EBPα-mimetics identified by interrogation of the Connectivity Map database. We found that amantadine, an antiviral and anti-Parkinson agent, induced a monocyte-macrophage-like differentiation of HL60, U937, Kasumi-1 myeloid leukemia cell lines, as indicated by morphology and differentiation antigen expression, when used in combination with suboptimal concentration of all trans retinoic acid (ATRA) or Vit D3. The effect of amantadine depends, in part, on increased activity of the vitamin D receptor (VDR), since it induced VDR expression and amantadine-dependent monocyte-macrophage differentiation of HL60 cells was blocked by expression of dominant-negative VDR. These results reveal a new function for amantadine and support the concept that screening of the Connectivity Map database can identify small molecules that mimic the effect of transcription factors required for myelo-monocytic differentiation