False Nearest Neighbor (FNN)
The false nearest neighbor algorithm is an algorithm for estimating the embedding dimension. The concept was proposed by Kennel et al. The main idea is to examine how the number of neighbors of a point along a signal trajectory change with increasing embedding dimension. In too low an embedding dimension, many of the neighbors will be false, but in an appropriate embedding dimension or higher, the neighbors are real. With increasing dimension, the false neighbors will no longer be neighbors. Therefore, by examining how the number of neighbors change as a function of dimension, an appropriate embedding can be determined. …

G-Learning
Model-free reinforcement learning algorithms such as Q-learning perform poorly in the early stages of learning in noisy environments, because much effort is spent on unlearning biased estimates of the state-action function. The bias comes from selecting, among several noisy estimates, the apparent optimum, which may actually be suboptimal. We propose G-learning, a new off-policy learning algorithm that regularizes the noise in the space of optimal actions by penalizing deterministic policies at the beginning of the learning. Moreover, it enables naturally incorporating prior distributions over optimal actions when available. The stochastic nature of G-learning also makes it more cost-effective than Q-learning in noiseless but exploration-risky domains. We illustrate these ideas in several examples where G-learning results in significant improvements of the learning rate and the learning cost. …

Contrastive Principal Component Analysis (cPCA)
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a generalization of standard PCA, for the setting where multiple datasets are available — e.g. a treatment and a control group, or a mixed versus a homogeneous population — and the goal is to explore patterns that are specific to one of the datasets. We conduct a wide variety of experiments in which cPCA identifies important dataset-specific patterns that are missed by PCA, demonstrating that it is useful for many applications: subgroup discovery, visualizing trends, feature selection, denoising, and data-dependent standardization. We provide geometrical interpretations of cPCA and show that it satisfies desirable theoretical guarantees. We also extend cPCA to nonlinear settings in the form of kernel cPCA. We have released our code as a python package and documentation is on Github. …