arXiv subjects

Tamara Broderick

Publications and source records attributed to Tamara Broderick.

95 records · Page 6Linked to original sources

arXiv2010

Classification and categorical inputs with treed Gaussian process models

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have, separately, enjoyed great success in application to classification problems. An example of the former is Bayesian CART. In the latter, real-valued GP output may be utilized for classification via latent variables, which provide classification rules by means of a softmax function. We formulate a Bayesian model averaging scheme to combine these two models and describe a Monte Carlo method for sampling from the full posterior distribution with joint proposals for the tree topology and the GP parameters corresponding to latent variables at the leaves. We concentrate on efficient sampling of the latent variables, which is important to obtain good mixing in the expanded parameter space. The tree structure is particularly helpful for this task and also for developing an efficient scheme for handling categorical predictors, which commonly arise in classification problems. Our proposed classification TGP (CTGP) methodology is illustrated on a collection of synthetic and real data sets. We assess performance relative to existing methods and thereby show how CTGP is highly flexible, offers tractable inference, produces rules that are easy to interpret, and performs well out of sample.

stat.ME↗

arXiv2010

Fast and flexible selection with a single switch

Selection methods that require only a single-switch input, such as a button click or blink, are potentially useful for individuals with motor impairments, mobile technology users, and individuals wishing to transmit information securely. We present a single-switch selection method, "Nomon," that is general and efficient. Existing single-switch selection methods require selectable options to be arranged in ways that limit potential applications. By contrast, traditional operating systems, web browsers, and free-form applications (such as drawing) place options at arbitrary points on the screen. Nomon, however, has the flexibility to select any point on a screen. Nomon adapts automatically to an individual's clicking ability; it allows a person who clicks precisely to make a selection quickly and allows a person who clicks imprecisely more time to make a selection without error. Nomon reaps gains in information rate by allowing the specification of beliefs (priors) about option selection probabilities and by avoiding tree-based selection schemes in favor of direct (posterior) inference. We have developed both a Nomon-based writing application and a drawing application. To evaluate Nomon's performance, we compared the writing application with a popular existing method for single-switch writing (row-column scanning). Novice users wrote 35% faster with the Nomon interface than with the scanning interface. An experienced user (author TB, with > 10 hours practice) wrote at speeds of 9.3 words per minute with Nomon, using 1.2 clicks per character and making no errors in the final text.

cs.HC↗

arXiv2007

Faster solutions of the inverse pairwise Ising problem

Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.

q-bio.QM↗

arXiv2006

Ellipticity of dark matter halos with galaxy-galaxy weak lensing

We present the results of attempts to detect the ellipticity of dark matter halos using galaxy-galaxy weak lensing with SDSS data. We use 2,020,256 galaxies brighter than r=19 with photometric redshifts (divided into colour and luminosity subsamples) as lenses and 31,697,869 source galaxies. We search for and identify several signal contaminants, which if not removed lead to a spurious detection. These include systematic shear that leads to a slight spurious alignment of lens and source ellipticities, intrinsic alignments (due to contamination of the source sample by physically-associated lens source pairs), and anisotropic magnification bias. We develop methods that allow us to remove these contaminants to the signal. We split the analysis into blue (spiral) and red (elliptical) galaxies. Assuming Gaussian errors as in previous work and a power-law profile, we find f_h=e_h/e_g=0.1+/-0.06 for red galaxies and -0.8+/-0.4 for blue galaxies using 20-300 kpc/h, averaged over luminosity. Inclusion of the more realistic non-Gaussian error distributions and of the NFW density profile (which predicts much smaller ellipticity of the shear for scales above the scale radius) yields 0.60+/-0.38 for ellipticals and -1.4+1.7-2.0 for spirals. While there is no concrete detection of alignment in either case, there is a suggestion in the data of a positive alignment in the brightest lens sample of ellipticals. Our results appear to be mildly inconsistent with a previously reported detection by Hoekstra et al. (2004), but more data and further tests are needed to clarify whether the discrepancy is real or a consequence of differences in the lens galaxy samples used and analysis methods.

astro-ph↗

arXiv2004

Redshift Accuracy Requirements for Future Supernova and Number Count Surveys

We investigate the required redshift accuracy of type Ia supernova and cluster number-count surveys in order for the redshift uncertainties not to contribute appreciably to the dark energy parameter error budget. For the SNAP supernova experiment, we find that, without the assistance of ground-based measurements, individual supernova redshifts would need to be determined to about 0.002 or better, which is a challenging but feasible requirement for a low-resolution spectrograph. However, we find that accurate redshifts for z<0.1 supernovae, obtained with ground-based experiments, are sufficient to immunize the results against even relatively large redshift errors at high z. For the future cluster number-count surveys such as the South Pole Telescope, Planck or DUET, we find that the purely statistical error in photometric redshift is less important, and that the irreducible, systematic bias in redshift drives the requirements. The redshift bias will have to be kept below 0.001-0.005 per redshift bin (which is determined by the filter set), depending on the sky coverage and details of the definition of the minimal mass of the survey. Furthermore, we find that X-ray surveys have a more stringent required redshift accuracy than Sunyaev-Zeldovich (SZ) effect surveys since they use a shorter lever arm in redshift; conversely, SZ surveys benefit from their high redshift reach only so long as some redshift information is available for distant (z>1) clusters.

astro-ph↗