TY  - JOUR
A1  - Katz-Samuels, Julian
A1  - Blanchard, Gilles
A1  - Scott, Clayton
T1  - Decontamination of Mutual Contamination Models
JF  - Journal of machine learning research
N2  - Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions and the goal is to infer these base distributions. This paper considers the general setting where the base distributions are defined on arbitrary probability spaces. We examine three popular machine learning problems that arise in this general setting: multiclass classification with label noise, demixing of mixed membership models, and classification with partial labels. In each case, we give sufficient conditions for identifiability and present algorithms for the infinite and finite sample settings, with associated performance guarantees.
KW  - multiclass classification with label noise
KW  - classification with partial labels
KW  - mixed membership models
KW  - topic modeling
KW  - mutual contamination models
Y1  - 2019
UR  - http://arxiv.org/abs/1710.01167
SN  - 1532-4435
VL  - 20
PB  - Microtome Publishing
CY  - Cambridge, Mass.
ER  - 
TY  - JOUR
A1  - Blanchard, Gilles
A1  - Zadorozhnyi, Oleksandr
T1  - Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process.
KW  - Banach-valued process
KW  - Bernstein inequality
KW  - concentration
KW  - spectral regularization
KW  - weak dependence
Y1  - 2019
U6  - https://doi.org/10.3150/18-BEJ1095
SN  - 1350-7265
SN  - 1573-9759
VL  - 25
IS  - 4B
SP  - 3421
EP  - 3458
PB  - International Statistical Institute
CY  - Voorburg
ER  -