A Unifying review of linear gaussian models

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

On the Reduction of Errors in DNA Computation

In this paper, we discuss techniques for reducing errors in DNA computation. We investigate several methods for achieving acceptable overall error rates for a computation using basic operations that are error prone. We analyze a single essential biotechnology, sequence-specific separation, and show that separation errors theoretically can be reduced to tolerable levels by invoking a tradeoff between time, space, and error rates at the level of algorithm design. These tradeoffs do not depend upon improvement of the underlying biotechnology which implements the separation step. We outline several specific ways in which error reduction can be done and present numerical calculations of their performance

Astrometry.net: Blind astrometric calibration of arbitrary astronomical images

We have built a reliable and robust system that takes as input an astronomical image, and returns as output the pointing, scale, and orientation of that image (the astrometric calibration or WCS information). The system requires no first guess, and works with the information in the image pixels alone; that is, the problem is a generalization of the "lost in space" problem in which nothing--not even the image scale--is known. After robust source detection is performed in the input image, asterisms (sets of four or five stars) are geometrically hashed and compared to pre-indexed hashes to generate hypotheses about the astrometric calibration. A hypothesis is only accepted as true if it passes a Bayesian decision theory test against a background hypothesis. With indices built from the USNO-B Catalog and designed for uniformity of coverage and redundancy, the success rate is 99.9% for contemporary near-ultraviolet and visual imaging survey data, with no false positives. The failure rate is consistent with the incompleteness of the USNO-B Catalog; augmentation with indices built from the 2MASS Catalog brings the completeness to 100% with no false positives. We are using this system to generate consistent and standards-compliant meta-data for digital and digitized imaging from plate repositories, automated observatories, individual scientific investigators, and hobbyists. This is the first step in a program of making it possible to trust calibration meta-data for astronomical data of arbitrary provenance.Comment: submitted to A

Bi-stochastic kernels via asymmetric affinity functions

In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in X and some reference set Y. Unlike other methods that construct bi-stochastic kernels via some convergent iteration process or through solving an optimization problem, the construction presented here is quite simple. Furthermore, it can be viewed through the lens of out of sample extensions, making it useful for massive data sets.Comment: 5 pages. v2: Expanded upon the first paragraph of subsection 2.1. v3: Minor changes and edits. v4: Edited comments and added DO

Inference with Constrained Hidden Markov Models in PRISM

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. Defining HMMs with side-constraints in Constraint Logic Programming have advantages in terms of more compact expression and pruning opportunities during inference. We present a PRISM-based framework for extending HMMs with side-constraints and show how well-known constraints such as cardinality and all different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment

Diffusion maps for changing data

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications.Comment: 38 pages. 9 figures. To appear in Applied and Computational Harmonic Analysis. v2: Several minor changes beyond just typos. v3: Minor typo corrected, added DO

Cleaning the USNO-B Catalog through automatic detection of optical artifacts

The USNO-B Catalog contains spurious entries that are caused by diffraction spikes and circular reflection halos around bright stars in the original imaging data. These spurious entries appear in the Catalog as if they were real stars; they are confusing for some scientific tasks. The spurious entries can be identified by simple computer vision techniques because they produce repeatable patterns on the sky. Some techniques employed here are variants of the Hough transform, one of which is sensitive to (two-dimensional) overdensities of faint stars in thin right-angle cross patterns centered on bright (<13 \mag) stars, and one of which is sensitive to thin annular overdensities centered on very bright (<7 \mag) stars. After enforcing conservative statistical requirements on spurious-entry identifications, we find that of the 1,042,618,261 entries in the USNO-B Catalog, 24,148,382 of them (2.3 \percent) are identified as spurious by diffraction-spike criteria and 196,133 (0.02 \percent) are identified as spurious by reflection-halo criteria. The spurious entries are often detected in more than 2 bands and are not overwhelmingly outliers in any photometric properties; they therefore cannot be rejected easily on other grounds, i.e., without the use of computer vision techniques. We demonstrate our method, and return to the community in electronic form a table of spurious entries in the Catalog.Comment: published in A

Blind Normalization of Speech From Different Channels

We show how to construct a channel-independent representation of speech that has propagated through a noisy reverberant channel. This is done by blindly rescaling the cepstral time series by a non-linear function, with the form of this scale function being determined by previously encountered cepstra from that channel. The rescaled form of the time series is an invariant property of it in the following sense: it is unaffected if the time series is transformed by any time-independent invertible distortion. Because a linear channel with stationary noise and impulse response transforms cepstra in this way, the new technique can be used to remove the channel dependence of a cepstral time series. In experiments, the method achieved greater channel-independence than cepstral mean normalization, and it was comparable to the combination of cepstral mean normalization and spectral subtraction, despite the fact that no measurements of channel noise or reverberations were required (unlike spectral subtraction).Comment: 25 pages, 7 figure