Ph. D. Project
Estimation of high dimensional probability density functions with low-rank tensor models: application to cancer cell characterization
2020/10/15 - 2024/04/30
The evolution of most cancers depends on their metastatic potential, which is unfortunately very difficult to predict due to dependence on multiple factors.
Various types of data, such as flow cytometry data [1] , AFM force volume images [2], or hyperspectral images can be used to characterize the metastatic potential of malignant cancer cells.
The core underlying problem can be cast as estimating the joint probability density of multivariate random variables, and becomes intractable due to curse of dimensionality, if no structure or relationship between the variables is assumed.
Nevertheless, for a class of latent variable models (e.g., naive Bayes model), the problem can be viewed as a low-rank decomposition of a probability mass tensor.
We propose to exploit the low-rank property for the problems of density estimation and classification.
In order to tackle the high-dimensionality of the problem, we propose to resort to (a) novel tensor network decompositions and (b) considering marginal distributions.

[1] Brie, D., et al., Joint analysis of flow cytometry data and fluorescence spectra as a non-negative array factorization problem, Chemometrics and Intelligent Laboratory Systems 137, 21-32, 2014.

[2] Barbieux, C., et al. "DDB2 (damaged-DNA binding 2) protein: a new modulator of nanomechanical properties and cell adhesion of breast cancer cells." Nanoscale 8.9 (2016): 5268-5279.
atrificial intelligence, density estimation, machine learning, tensor methods
Biology, Signals and Systems in Cancer and Neuroscience