High-dimensional change-point detection with sparse alternatives

We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a change-point that is adaptive to the number of changing components. Under the assumption that the vector dimension tends to infinity and the length of the sequence grows slower than the dimension of the signal, we obtain the detection boundary for this problem and prove its rate-optimality

Yield Improvement by the Redundancy Method for Component Calibration

3 pagesInternational audienceWe explore the benefits of a redundant channels methodology for the component calibration. We propose a normal approximation of the yield in order to estimate the number of redundant components needed to provide a minimal area occupied by the components

A model of evolution with constant selective pressure for regulatory DNA sites

<p>Abstract</p> <p>Background</p> <p>Molecular evolution is usually described assuming a neutral or weakly non-neutral substitution model. Recently, new data have become available on evolution of sequence regions under a selective pressure, e.g. transcription factor binding sites. To reconstruct the evolutionary history of such sequences, one needs evolutionary models that take into account a substantial constant selective pressure.</p> <p>Results</p> <p>We present a simple evolutionary model with a single preferred (consensus) nucleotide and the neutral substitution model adopted for all other nucleotides. This evolutionary model has a rate matrix in which all substitutions that do not involve the consensus nucleotide occur with the same rate. The model has two time scales for achieving a stationary distribution; in the general case only one of the two rate parameters can be evaluated from the stationary distribution. In the middle-time zone, a counterintuitive behavior was observed for some parameter values, with a probability of conservation for a non-consensus nucleotide greater than that for the consensus nucleotide. Such an effect can be observed only in the case of weak preference for the consensus nucleotide, when the probability to observe the consensus nucleotide in the stationary distribution is less than 1/2. If the substitution rate is represented as a product of mutation and fixation, only the fixation can be calculated from the stationary distribution. The exhibited conservation of non-consensus nucleotides does not take place if the elements of mutation matrix are identical, and can be related to the reduced mutation rate between the non-consensus nucleotides. This bias can have no effect on the stationary distribution of nucleotide frequencies calculated over the ensemble of multiple alignments, e.g. transcription factor binding sites upstream of different sets of co-regulated orthologous genes.</p> <p>Conclusion</p> <p>The derived model can be used as a null model when analyzing the evolution of orthologous transcription factor binding sites. In particular, our findings show that a nucleotide preferred at some position of a multiple alignment of binding sites for some transcription factor in the same genome is not necessarily the most conserved nucleotide in an alignment of orthologous sites from different species. However, this effect can take place only in the case of a mutation matrix whose elements are not identical.</p

Change-point detection, segmentation, and related topics

Recent contributions to change-point detection, segmentation and inference for non-regular models are presented. Various problems are considered including the multiple change-point estimation with adaptive penalty for time series with different dependency structures, estimation of the singularity point in cusp-type models, inference for thresholded autoregressive models, and cross-segmentation of matrices

Adaptive minimax estimation of a fractional derivative Adaptive minimax estimation of a fractional derivative

Abstract In this paper we consider a problem of adaption in estimating a fractional derivative of an unknown density from observations in the Gaussian white noise. This problem is closely related to the Wicksell problem. Under the assumption that density belongs to a Sobolev class with unknown smoothness, an adaptive estimator is constructed

Change-Point Detection in Dynamic Networks with Missing Links

Structural changes occur in dynamic networks quite frequently and its detection is an important question in many situations such as fraud detection or cybersecurity. Real-life networks are often incompletely observed due to individual non-response or network size. In the present paper we consider the problem of change-point detection at a temporal sequence of partially observed networks. The goal is to test whether there is a change in the network parameters. Our approach is based on the Matrix CUSUM test statistic and allows growing size of networks. We show that the proposed test is minimax optimal and robust to missing links. We also demonstrate the good behavior of our approach in practice through simulation study and a real-data application