[Paper Review] Unsupervised feature extraction by time-contrastive learning and nonlinear ICA

Aapo Hyvärinen, Hiroshi Morioka|arXiv (Cornell University)|Dec 5, 2016

Blind Source Separation Techniques31 references137 citations

TL;DR

This paper introduces time-contrastive learning (TCL), a novel unsupervised deep learning principle that leverages temporal nonstationarities in time series to extract meaningful features. TCL enables identifiability in nonlinear ICA by estimating sources up to point-wise transformations, providing the first rigorous, constructive, and general identifiability result for nonlinear ICA models.

ABSTRACT

Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our learning principle, time-contrastive learning (TCL), finds a representation which allows optimal discrimination of time segments (windows). Surprisingly, we show how TCL can be related to a nonlinear ICA model, when ICA is redefined to include temporal nonstationarities. In particular, we show that TCL combined with linear ICA estimates the nonlinear ICA model up to point-wise transformations of the sources, and this solution is unique — thus providing the first identifiability result for nonlinear ICA which is rigorous, constructive, as well as very general.

Motivation & Objective

• To address the lack of identifiability in existing nonlinear ICA models for unsupervised feature learning.
• To develop a new principle for deep unsupervised learning using the nonstationary structure of time series data.
• To establish a connection between time-contrastive learning and nonlinear ICA under a redefined framework that includes temporal nonstationarities.
• To provide a rigorous, constructive, and general identifiability result for nonlinear ICA, ensuring unique estimation of sources up to point-wise transformations.

Proposed method

• Proposes time-contrastive learning (TCL), which learns representations by contrasting different time segments (windows) of a time series.
• Uses a contrastive objective that encourages the model to distinguish between time segments while preserving invariant representations.
• Reinterprets nonlinear ICA to include temporal nonstationarities, enabling the connection between TCL and ICA frameworks.
• Combines TCL with linear ICA to estimate the nonlinear ICA model, ensuring identifiability up to point-wise transformations of the sources.
• Employs a representation learning objective that maximizes discrimination between time windows while preserving structural invariance.
• Demonstrates that the solution is unique under mild regularity conditions, establishing the first general identifiability result for nonlinear ICA.

Experimental results

Research questions

• RQ1 Can temporal nonstationarities in time series be exploited to create a new principle for unsupervised deep learning?
• RQ2 How can time-contrastive learning be formally connected to nonlinear ICA when ICA is extended to include nonstationarities?
• RQ3 Is the solution obtained via TCL combined with linear ICA identifiable in the context of nonlinear ICA?
• RQ4 What conditions ensure the uniqueness of the learned representation in this framework?
• RQ5 Can this approach achieve identifiability for nonlinear ICA models in a general and constructive manner?

Key findings

• Time-contrastive learning (TCL) successfully extracts features by contrasting time segments, leveraging the nonstationary structure of time series.
• TCL is formally linked to a redefined nonlinear ICA model that incorporates temporal nonstationarities.
• The combination of TCL and linear ICA provides a unique solution for nonlinear ICA up to point-wise transformations of the sources.
• This solution is the first to achieve rigorous, constructive, and general identifiability in nonlinear ICA.
• The method establishes a new foundation for unsupervised feature learning with strong theoretical guarantees.