A sparse kernel density estimation algorithm using forward constrained regression

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward constrained regression manner. The leave-one-out (LOO) test score is used for kernel selection. The jackknife parameter estimator subject to positivity constraint check is used for the parameter estimation of a single parameter at each forward step. As such the proposed approach is simple to implement and the associated computational cost is very low. An illustrative example is employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to that of the classical Parzen window estimate.

A forward-constrained regression algorithm for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward-constrained regression (FCR) manner. The proposed algorithm selects significant kernels one at a time, while the leave-one-out (LOO) test score is minimized subject to a simple positivity constraint in each forward stage. The model parameter estimation in each forward stage is simply the solution of jackknife parameter estimator for a single parameter, subject to the same positivity constraint check. For each selected kernels, the associated kernel width is updated via the Gauss-Newton method with the model parameter estimate fixed. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Adding a receding horizon to Locally Weighted Regression for learning robot control

There have been notable advances in learning to control complex robotic systems using methods such as Locally Weighted Regression (LWR). In this paper we explore some potential limits of LWR for robotic applications, particularly investigating its application to systems with a long horizon of temporal dependence. We define the horizon of temporal dependence as the delay from a control input to a desired change in output. LWR alone cannot be used in a temporally dependent system to find meaningful control values from only the current state variables and output, as the relationship between the input and the current state is under-constrained. By introducing a receding horizon of the future output states of the system, we show that sufficient constraint is applied to learn good solutions through LWR. The new method, Receding Horizon Locally Weighted Regression (RH-LWR), is demonstrated through one-shot learning on a real Series Elastic Actuator controlling a pendulum.

Adolescent self-reported physical activity and autonomy: A case for constrained and structured environments?

The provision of autonomy supportive environments that promote physical activity engagement have become popular in contemporary youth settings. However, questions remain about whether adolescent perceptions of their autonomy have implications for physical activity. The purpose of this investigation was to examine the association between adolescents’ self-reported physical activity and their perceived autonomy. Participants (n = 384 adolescents) aged between 12 and 15 years were recruited from six secondary schools in metropolitan Brisbane, Australia. Self-reported measures of physical activity and autonomy were obtained. Logistic regression with inverse probability weights were used to examine the association between autonomy and the odds of meeting youth physical activity guidelines. Autonomy (OR 0.61, 95% CI 0.49-0.76) and gender (OR 0.62, 95% CI 0.46-0.83) were negatively associated with meeting physical activity guidelines. However, the model explained only a small amount of the variation in whether youth in this sample met physical activity guidelines (R2 = 0.023). For every 1 unit decrease in autonomy (on an index from 1 to 5), participants were 1.64 times more likely to meet physical activity guidelines. The findings, which are at odds with several previous studies, suggest that interventions designed to facilitate youth physical activity should limit opportunities for youth to make independent decisions about their engagement. However, the small amount of variation explained by the predictors in the model is a caveat, and should be considered prior to applying such suggestions in practical settings. Future research should continue to examine a larger age range, longitudinal observational or intervention studies to examine assertions of causality, as well as objective measurement of physical activity.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

How Porosity and Permeability Vary Spatially With Grain Size, Sorting, Cement Volume, and Mineral Dissolution In Fluvial Triassic Sandstones: The Value of Geostatistics and Local Regression

Although it is well known that sandstone porosity and permeability are controlled by a range of parameters such as grain size and sorting, amount, type, and location of diagenetic cements, extent and type of compaction, and the generation of intergranular and intragranular secondary porosity, it is less constrained how these controlling parameters link up in rock volumes (within and between beds) and how they spatially interact to determine porosity and permeability. To address these unknowns, this study examined Triassic fluvial sandstone outcrops from the UK using field logging, probe permeametry of 200 points, and sampling at 100 points on a gridded rock surface. These field observations were supplemented by laser particle-size analysis, thin-section point-count analysis of primary and diagenetic mineralogy, quantitiative XRD mineral analysis, and SEM/EDAX analysis of all 100 samples. These data were analyzed using global regression, variography, kriging, conditional simulation, and geographically weighted regression to examine the spatial relationships between porosity and permeability and their potential controls. The results of bivariate analysis (global regression) of the entire outcrop dataset indicate only a weak correlation between both permeability porosity and their diagenetic and depositional controls and provide very limited information on the role of primary textural structures such as grain size and sorting. Subdividing the dataset further by bedding unit revealed details of more local controls on porosity and permeability. An alternative geostatistical approach combined with a local modelling technique (geographically weighted regression; GWR) subsequently was used to examine the spatial variability of porosity and permeability and their controls. The use of GWR does not require prior knowledge of divisions between bedding units, but the results from GWR broadly concur with results of regression analysis by bedding unit and provide much greater clarity of how porosity and permeability and their controls vary laterally and vertically. The close relationship between depositional lithofacies in each bed, diagenesis, and permeability, porosity demonstrates that each influences the other, and in turn how understanding of reservoir properties is enhanced by integration of paleoenvironmental reconstruction, stratigraphy, mineralogy, and geostatistics.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Mortality associated with discordant responses to antiretroviral therapy in resource-constrained settings

Objectives: We assessed mortality associated with immunologic and virologic patterns of response at 6 months of highly active antiretroviral therapy (HAART) in HIV-infected individuals from resource-limited countries in Africa and South America. Methods: Patients who initiated HAART between 1996 and 2007, aged 16 years or older, and had at least 1 measurement (HIV-1 RNA plasma viral load or CD4 cell count) at 6 months of therapy (3-9 month window) were included. Therapy response was categorized as complete, discordant (virologic only or immunologic only), and absent. Associations between 6-month response to therapy and all-cause mortality were assessed by Cox proportional hazards regression. Robust standard errors were calculated to account for intrasite correlation. Results: A total of 7160 patients, corresponding to 15,107 person-years, were analyzed. In multivariable analysis adjusted for age at HAART initiation, baseline clinical stage and CD4 cell count, year of HAART initiation, clinic, occurrence of an AIDS-defining condition within the first 6 months of treatment, and discordant and absent responses were associated with increased risk of death. Conclusions: Similar to reports from high-income countries, discordant immunologic and virologic responses were associated with intermediate risk of death compared with complete and no response in this large cohort of HIV-1 patients from resource-limited countries. Our results support a recommendation for wider availability of plasma viral load testing to monitor antiretroviral therapy in these settings.

Discordant responses to potent antiretroviral treatment in previously naive HIV-1-infected adults initiating treatment in resource-constrained countries: the antiretroviral therapy in low-income countries (ART-LINC) collaboration

OBJECTIVES: To assess the frequency of and risk factors for discordant responses at 6 months on highly active antiretroviral therapy (HAART) in previously treatment-naive HIV patients from resource-limited countries. METHODS: The Antiretroviral Therapy in Low-Income Countries Collaboration is a network of clinics providing care and treatment to HIV-infected patients in Africa, Latin America, and Asia. Patients who initiated therapy between 1996 and 2004, were aged 16 years or older, and had a baseline CD4 cell count were included in this analysis. Responses were defined based on plasma viral load (PVL) and CD4 cell count at 6 months as complete virologic and immunologic (VR(+)IR(+)), virologic only (VR(+)IR(-)), immunologic only (VR(-)IR(+)), and nonresponse (VR(-)IR(-)). Multinomial logistic regression was used to assess the association between therapy responses and clinical and demographic variables. RESULTS: Of the 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VR(+)IR(+), 364 (19.0%) were VR(+)IR(-), 283 (14.8%) were (VR(-)IR(+)), and 193 (10.1%) were VR(-)IR(-). OF THE 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VRIR, 364 (19.0%) were VRIR, 283 (14.8%) were (VRIR), and 193 (10.1%) were VRIR. Compared with complete responders, virologic-only responders were older, had a higher baseline CD4 cell count, had a lower baseline PVL, and were more likely to have received a nonstandard HAART regimen; immunologic-only responders were younger, had a lower baseline CD4 cell count, had a higher baseline PVL, and were more likely to have received a protease inhibitor-based regimen. CONCLUSIONS: The frequency of and risk factors for discordant responses were comparable to those observed in developed countries. Longer follow-up is needed to assess the long-term impact of discordant responses on mortality in these resource-limited settings.

Zircons, isotope ratios and element analyses from tonalite and oxide gabbro of the mid-ocean ridge from ODP Hole 176-735B

A limiting factor in the accuracy and precision of U/Pb zircon dates is accurate correction for initial disequilibrium in the 238U and 235U decay chains. The longest-lived-and therefore most abundant-intermediate daughter product in the 235U isotopic decay chain is 231Pa (T1/2 = 32.71 ka), and the partitioning behavior of Pa in zircon is not well constrained. Here we report high-precision thermal ionization mass spectrometry (TIMS) U-Pb zircon data from two samples from Ocean Drilling Program (ODP) Hole 735B, which show evidence for incorporation of excess 231Pa during zircon crystallization. The most precise analyses from the two samples have consistent Th-corrected 206Pb/238U dates with weighted means of 11.9325 ± 0.0039 Ma (n = 9) and 11.920 ± 0.011 Ma (n = 4), but distinctly older 207Pb/235U dates that vary from 12.330 ± 0.048 Ma to 12.140 ± 0.044 Ma and 12.03 ± 0.24 to 12.40 ± 0.27 Ma, respectively. If the excess 207Pb is due to variable initial excess 231Pa, calculated initial (231Pa)/(235U) activity ratios for the two samples range from 5.6 ± 1.0 to 9.6 ± 1.1 and 3.5 ± 5.2 to 11.4 ± 5.8. The data from the more precisely dated sample yields estimated DPazircon/DUzircon from 2.2-3.8 and 5.6-9.6, assuming (231Pa)/(235U) of the melt equal to the global average of recently erupted mid-ocean ridge basaltic glasses or secular equilibrium, respectively. High precision ID-TIMS analyses from nine additional samples from Hole 735B and nearby Hole 1105A suggest similar partitioning. The lower range of DPazircon/DUzircon is consistent with ion microprobe measurements of 231Pa in zircons from Holocene and Pleistocene rhyolitic eruptions (Schmitt (2007; doi:10.2138/am.2007.2449) and Schmitt (2011; doi:10.1146/annurev-earth-040610-133330)). The data suggest that 231Pa is preferentially incorporated during zircon crystallization over a range of magmatic compositions, and excess initial 231Pa may be more common in zircons than acknowledged. The degree of initial disequilibrium in the 235U decay chain suggested by the data from this study, and other recent high precision datasets, leads to resolvable discordance in high precision dates of Cenozoic to Mesozoic zircons. Minor discordance in zircons of this age may therefore reflect initial excess 231Pa and does not require either inheritance or Pb loss.

Chemistry and age determination of basement fluids from Juan de Fuca Ridge

The geochemical implications of thermally driven flow of seawater through oceanic crust on the mid-ocean ridge flank have been examined on a well-studied 80 km transect across the eastern flank of the Juan de Fuca Ridge at 48°N, using porewater and basement fluid samples obtained on ODP Leg 168. Fluid flow is recognised by near-basement reversals in porewater concentration gradients from altered values in the sediment section to seawater-like values in basaltic basement. In general, the basement fluids become more geochemically evolved with distance from the ridge and broadly follow basement temperature which ranges from not, vert, similar16° to 63°C. Although thermal effects of advective heat exchange are only seen within 20 km east of where basement is exposed near the ridge crest, chemical reactivity extends to all sites. Seawater passing through oceanic crust has reacted with basement rocks leading to increases in Ca2+ and decreases in alkalinity, Mg2+, Na+, K+, SO42- and delta18O. Sr isotope exchange between seawater and oceanic crust off axis is unequivocally demonstrated with endmember 87Sr/86Sr ~ 0.707. Evidence of more evolved fluids is seen at sites where rapid upwelling of fluids through sediments occurs. Chlorinities of the basement fluids are consistent with post-glacial seawater and thus a short residence time in the crust. Rates of lateral flow have been by estimated by modelling porewater sulphate gradients, using Cl as a glacial chronometer, and from radiocarbon dating of basal fluids. All three methods reveal fluid flow with 14C ages less than 10,000 yr and particle velocities of ~1-5 m/yr, in agreement with thermally constrained volumetric flow rates through a ~600 m thick permeable layer of ~10% porosity. Delta(element)/Delta(heat) extraction ratios are similar to values for ridge-crest hydrothermal systems.

Strontium isotope ratios of planktonic foraminifera from sediment samples acroos the K/T boundary

Seawater 87Sr/86Sr values increase abruptly by 28 * 10**-6 across the Cretaceous/Tertiary boundary (KTB). This small, but rapid shift is superimposed on the larger scale structure of the seawater Sr isotope curve. The time scale of radiogenic Sr addition appears to be too rapid to reconcile with sources associated with volcanism, and we show that the amount of Sr required to produce even this small increase is too large to be derived from: (1) a KT bolide of the size constrained by the Ir anomaly, (2) continental crust ejecta from the impact of such a bolide, (3) soot from global wildfires initiated by an impact, or (4) any combination of these sources. The probable source of the radiogenic Sr is enhanced continental weathering, but the high rate of increase appears to rule out processes such as sea level regression, glaciation or tectonism. A plausible mechanism for rapid addition of radiogenic Sr to the oceans is enhanced weathering associated with globally distributed acid rain (pH c. 1) which is a proposed by-product of a bolide impact (Prinn and Fegley, 1987, doi:10.1016/0012-821X(87)90046-X).

Mg/Ca and stable oxygen measurement of the past 27 Ma of ODP Hole 120-747A

We explore the applicability of paired Mg/Ca and 18O/16O measurements on benthic foraminifera from Southern Ocean site 747 to paleoceanographic reconstructions on pre-Pleistocene timescales. We focus on the late Oligocene through Pleistocene (27-0 Ma) history of paleotemperatures and the evolution of the d18O values of seawater (d18Osw) at a temporal resolution of ~100-200 kyr. Absolute paleotemperature estimates depend on assumptions of how Mg/Ca ratios of seawater have changed over the past 27 Myr, but relative changes that occur on geologically brief timescales are robust. Results indicate that at the Oligocene to Miocene boundary (23.8 Ma), temperatures lag the increase in global ice-volume deduced from benthic foraminiferal d18O values, but the smaller-scale Miocene glaciations are accompanied by ocean cooling of -1°C. During the mid-Miocene phase of Antarctic ice sheet growth (~15-13 Ma), water temperatures cool by ~3°C. Unlike the benthic foraminiferal d18O values, which remain relatively constant thereafter, temperatures vary (by 3°C) and reach maxima at ~12 and ~8.5 Ma. The onset of significant Northern Hemisphere glaciation during the late Pliocene is synchronous with an ~4°C cooling at site 747. A comparison of our d18Osw curve to the Haq et al. (1987, doi:10.1126/science.235.4793.1156 ) sea level curve yields excellent agreement between sequence boundaries and times of increasing seawater 18O/16O ratios. At ~12-11 Ma in particular, when benthic foraminiferal d18O values do not support a further increase in ice volume, the d18Osw curve comes to a maximum that corresponds to a major mid-Miocene sea level regression. The agreement between the character of our Mg/Ca-based d18Osw curve and sequence stratigraphy demonstrates that benthic foramaniferal Mg/Ca ratios can be used to trace the d18Osw on pre-Pleistocene timescales despite a number of uncertainties related to poorly constrained temperature calibrations and paleoseawater Mg/Ca ratios. The Mg/Ca record also highlights that deep ocean temperatures can vary independently and unexpectedly from ice volume changes, which can lead to misinterpretations of the d18O record.