Unsupervised Regression with Applications to Nonlinear System Identification

We derive a cost functional for estimating the relationship between high-dimensional observations and the low-dimensional process that generated them with no input-output examples. Limiting our search to invertible observation functions confers numerous benefits, including a compact representation and no suboptimal local minima. Our approximation algorithms for optimizing this cost functional are fast and give diagnostic bounds on the quality of their solution. Our method can be viewed as a manifold learning algorithm that utilizes a prior on the low-dimensional manifold coordinates. The benefits of taking advantage of such priors in manifold learning and searching for the inverse observation functions in system identification are demonstrated empirically by learning to track moving targets from raw measurements in a sensor network setting and in an RFID tracking experiment

Learning to Transform Time Series with a Few Examples

We describe a semi-supervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from sensors is transformed to a time series describing the pose of a target. Instead of defining and implementing such transformations for each tracking task separately, our algorithm learns a memoryless transformation of time series from a few example input-output mappings. The algorithm searches for a smooth function that fits the training examples and, when applied to the input time series, produces a time series that evolves according to assumed dynamics. The learning procedure is fast and lends itself to a closed-form solution. It is closely related to nonlinear system identification and manifold learning techniques. We demonstrate our algorithm on the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. For these tasks, this algorithm requires significantly fewer examples compared to fully-supervised regression algorithms or semi-supervised learning algorithms that do not take the dynamics of the output time series into account

viSNE and Wanderlust, two algorithms for the visualization and analysis of high-dimensional single-cell data

The immune system presents a unique opportunity for studying development in mammals. White blood cells undergo differentiation and proliferation, a never-ending process throughout the life of the organism. Hematopoiesis, the development of cells in the immune system, depends upon the interaction between many different cell types (some of which comprise less than a tenth of a percent of the population), transient regulatory decisions, genomic rearrangement events, cell proliferation, and death. To capture these events we employ mass cytometry, a novel technology that measures fifty proteins simultaneously in single cells. Mass cytometry results in large quantities of high-dimensional data which challenges existing computational techniques. To address these challenges, we developed two dimensionality reduction algorithms for analyzing mass cytometry and other single-cell data. The first, viSNE, transforms high-dimensional data into an intuitive two-dimensional map, making it accessible to visual exploration. The second algorithm, Wanderlust, receives as input a static snapshot (where cells occupy different stages of their development) and constructs their developmental ordering: the developmental trajectory. viSNE maps healthy bone marrow into a canonical shape that separates cell subtypes. In leukemia, however, the shape is malformed: the maps of cancer samples are distinct from the healthy map and from each other. The algorithm highlights structure in the heterogeneity of surface phenotype expression in cancer, traverses the progression from diagnosis to relapse, and identifies a rare leukemia population in minimal residual disease settings. Wanderlust was applied to healthy B lineage cells, where the trajectory follows known marker expression trends and genetic recombination events. Using the Wanderlust trajectory we identified CD24 as an early marker of B cell development. The trajectory captures the coordination between several regulatory mechanisms (surface marker expression, signaling, proliferation and apoptosis) during crucial development checkpoints. As new technologies raise the number of simultaneously measured parameters in each cell to the hundreds, viSNE and Wanderlust will become a mainstay in analyzing and interpreting such experiments

ENSO dynamics in current climate models: an investigation using nonlinear dimensionality reduction

International audienceLinear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. Here, we apply Isomap, one such technique, to the study of El Niño/Southern Oscillation variability in tropical Pacific sea surface temperatures, comparing observational data with simulations from a number of current coupled atmosphere-ocean general circulation models. We use Isomap to examine El Niño variability in the different datasets and assess the suitability of the Isomap approach for climate data analysis. We conclude that, for the application presented here, analysis using Isomap does not provide additional information beyond that already provided by principal component analysis