Partial Trace Regression and Low-Rank Kraus Decomposition

The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems

CAPweb: a bioinformatics CGH array Analysis Platform

Assessing variations in DNA copy number is crucial for understanding constitutional or somatic diseases, particularly cancers. The recently developed array-CGH (comparative genomic hybridization) technology allows this to be investigated at the genomic level. We report the availability of a web tool for analysing array-CGH data. CAPweb (CGH array Analysis Platform on the Web) is intended as a user-friendly tool enabling biologists to completely analyse CGH arrays from the raw data to the visualization and biological interpretation. The user typically performs the following bioinformatics steps of a CGH array project within CAPweb: the secure upload of the results of CGH array image analysis and of the array annotation (genomic position of the probes); first level analysis of each array, including automatic normalization of the data (for correcting experimental biases), breakpoint detection and status assignment (gain, loss or normal); validation or deletion of the analysis based on a summary report and quality criteria; visualization and biological analysis of the genomic profiles and results through a user-friendly interface. CAPweb is accessible at

Spatial normalization of array-CGH data

BACKGROUND: Array-based comparative genomic hybridization (array-CGH) is a recently developed technique for analyzing changes in DNA copy number. As in all microarray analyses, normalization is required to correct for experimental artifacts while preserving the true biological signal. We investigated various sources of systematic variation in array-CGH data and identified two distinct types of spatial effect of no biological relevance as the predominant experimental artifacts: continuous spatial gradients and local spatial bias. Local spatial bias affects a large proportion of arrays, and has not previously been considered in array-CGH experiments. RESULTS: We show that existing normalization techniques do not correct these spatial effects properly. We therefore developed an automatic method for the spatial normalization of array-CGH data. This method makes it possible to delineate and to eliminate and/or correct areas affected by spatial bias. It is based on the combination of a spatial segmentation algorithm called NEM (Neighborhood Expectation Maximization) and spatial trend estimation. We defined quality criteria for array-CGH data, demonstrating significant improvements in data quality with our method for three data sets coming from two different platforms (198, 175 and 26 BAC-arrays). CONCLUSION: We have designed an automatic algorithm for the spatial normalization of BAC CGH-array data, preventing the misinterpretation of experimental artifacts as biologically relevant outliers in the genomic profile. This algorithm is implemented in the R package MANOR (Micro-Array NORmalization), which is described at and available from the Bioconductor site . It can also be tested on the CAPweb bioinformatics platform at

Partial Trace Regression and Low-Rank Kraus Decomposition

The trace regression model, a direct extension of the well-studied linear regression model, al-lows one to map matrices to real-valued outputs.We here introduce an even more general model,namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps.We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.Peer reviewe

Partial Trace Regression and Low-Rank Kraus Decomposition

International audienceThe trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems

Partial Trace Regression and Low-Rank Kraus Decomposition

International audienceThe trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems

Tumor genomic profiling and TP53 germline mutation analysis of first-degree relative familial gliomas.

International audienceAbout 5% of gliomas occur in a familial context, which suggests a genetic origin, but the predisposing molecular factors remain unknown in most cases. A series of nine familial gliomas were characterized with 1-megabase resolution BAC array-based comparative genomic hybridization (aCGH) together with germline sequence analysis of TP53. This series was compared with a literature series of familial gliomas and a personal series of sporadic gliomas, analyzed by chromosome CGH and aCGH, respectively. No significant difference was noted between the three populations in terms of clinical characteristics, pathologic features, and the most frequent chromosomal alterations, including loss of 1p, 10p, 10q, 13q, and 19q, and gain of 7p, 7q, 16p, 18q, 19p, 19q, 20p, and 22q. However, a genomic region located in 6q was more frequently gained in our series of familial as compared to sporadic gliomas (P=0.028). A germline TP53 mutation was observed in 1/9 cases, which suggests Li-Fraumeni syndrome. Interestingly, the Pro allele in the codon 72 of TP53 was observed in 5/9 tumors. Although familial and sporadic gliomas share very similar cytogenetic quantitative patterns, aCGH is a promising technique for the detection of small genomic differences of potential significance