2,965 research outputs found
Boosting Additive Models using Component-wise P-Splines
We consider an efficient approximation of BĆ¼hlmann & Yuās L2Boosting algorithm with component-wise smoothing splines. Smoothing spline base-learners are replaced by P-spline base-learners which yield similar prediction errors but are more advantageous from a computational point of view. In particular, we give a detailed analysis on the effect of various P-spline hyper-parameters on the boosting fit. In addition, we derive a new theoretical result on the relationship between the boosting stopping iteration and the step length factor used for shrinking the boosting estimates
There is no simulation of n-qubit operations by a single Hamiltonian with 2-spin interaction
Today's devices for quantum computing are still far from implementing useful
and powerful quantum algorithms. Decoherence and the wish to resist the effects
of errors in a system of quantum bits incurs a lot of overhead in the number of
gates and qubits. From a theoretical perspective, controlled quantum simulation
raises the hope to simulate the unitary quantum operationes generated by a
Hamiltonian with 3-body interaction with a suitably designed element that is
constructed of only 2-body interactions. That replacement would happen without
any additional gates, and its possibility would be due to the ambiguity of the
unit element of the Lie group connected with the algebra of traceless hermitian
matrices. We show that this hope is void, and give a general proof for this for
any order of interaction.Comment: 4 pages, ReVTeX4, twocolum
Magnetic properties and spin waves of bilayer magnets in a uniform field
The two-layer square lattice quantum antiferromagnet with spins 1/2 shows a
zero-field magnetic order-disorder transition at a critical ratio of the
inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the
system to canted antiferromagnetism and eventually to a fully polarized state;
similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond
operator spin representation, we propose an approximate ground state
wavefunction which covers all phases by means of a unitary transformation. The
excitations can be efficiently described as independent bosons; in the
antiferromagnetic phase these reduce to the well-known spin waves, whereas they
describe gapped spin-1 excitations in the singlet phase. We compute the spectra
of these excitations as well as the magnetizations throughout the whole phase
diagram.Comment: 12 pages, 9 figs; added references; final version as publishe
Estimation and Regularization Techniques for Regression Models with Multidimensional Prediction Functions
Boosting is one of the most important methods for fitting
regression models and building prediction rules from
high-dimensional data. A notable feature of boosting is that the
technique has a built-in mechanism for shrinking coefficient
estimates and variable selection. This regularization mechanism
makes boosting a suitable method for analyzing data characterized by
small sample sizes and large numbers of predictors. We extend the
existing methodology by developing a boosting method for prediction
functions with multiple components. Such multidimensional functions
occur in many types of statistical models, for example in count data
models and in models involving outcome variables with a mixture
distribution. As will be demonstrated, the new algorithm is suitable
for both the estimation of the prediction function and
regularization of the estimates. In addition, nuisance parameters
can be estimated simultaneously with the prediction function
A PAUC-based Estimation Technique for Disease Classification and Biomarker Selection.
The partial area under the receiver operating characteristic curve (PAUC) is a well-established performance measure to evaluate biomarker combinations for disease classification. Because the PAUC is defined as the area under the ROC curve within a restricted interval of false positive rates, it enables practitioners to quantify sensitivity rates within pre-specified specificity ranges. This issue is of considerable importance for the development of medical screening tests. Although many authors have highlighted the importance of PAUC, there exist only few methods that use the PAUC as an objective function for finding optimal combinations of biomarkers. In this paper, we introduce a boosting method for deriving marker combinations that is explicitly based on the PAUC criterion. The proposed method can be applied in high-dimensional settings where the number of biomarkers exceeds the number of observations. Additionally, the proposed method incorporates a recently proposed variable selection technique (stability selection) that results in sparse prediction rules incorporating only those biomarkers that make relevant contributions to predicting the outcome of interest. Using both simulated data and real data, we demonstrate that our method performs well with respect to both variable selection and prediction accuracy. Specifically, if the focus is on a limited range of specificity values, the new method results in better predictions than other established techniques for disease classification
A Framework for Unbiased Model Selection Based on Boosting
Variable selection and model choice are of major concern in many statistical applications, especially in high-dimensional regression models. Boosting is a convenient statistical method that combines model fitting with intrinsic model selection.
We investigate the impact of base-learner specification on the performance of boosting as a model selection procedure.
We show that variable selection may be biased if the covariates are of different nature.
Important examples are models combining continuous and categorical covariates, especially if the number of categories is large. In this case, least squares base-learners offer increased flexibility for the categorical covariate and lead to a preference even if the categorical covariate is non-informative.
Similar difficulties arise when comparing linear and nonlinear base-learners for a continuous covariate. The additional flexibility in the nonlinear base-learner again yields a preference of the more complex modeling alternative.
We investigate these problems from a theoretical perspective and suggest a framework for unbiased model selection based on a general class of penalized least squares base-learners.
Making all base-learners comparable in terms of their degrees of freedom strongly reduces the selection bias observed in naive boosting specifications. The importance of unbiased model selection is demonstrated in simulations and an application to forest health models
Analysis of GRACE range-rate residuals with focus on KBR instrument system noise
We investigate the post-fit range-rate residuals after the gravity field
parameter estimation from the inter-satellite ranging data of the gravity
recovery and climate experiment (GRACE) satellite mission. Of particular
interest is the high-frequency spectrum (f gt 20 MHz) which is dominated by the
microwave ranging system noise. Such analysis is carried out to understand the
yet unsolved discrepancy between the predicted baseline errors and the observed
ones. The analysis consists of two parts. First, we present the effects in the
signal-to-noise ratio (SNRs) of the k-band ranging system. The SNRs are also
affected by the moon intrusions into the star cameras field of view and
magnetic torque rod currents in addition to the effects presented by Harvey et
al. [2016]. Second, we analyze the range-rate residuals to study the effects of
the KBR system noise. The range-rate residuals are dominated by the
non-stationary errors in the high-frequency observations. These high-frequency
errors in the range-rate residuals are found to be dependent on the temperature
and effects of sun intrusion into the star cameras field of view reflected in
the SNRs of the K-band phase observations
Theory of filtered type-II PDC in the continuous-variable domain: Quantifying the impacts of filtering
Parametric down-conversion (PDC) forms one of the basic building blocks for
quantum optical experiments. However, the intrinsic multimode spectral-temporal
structure of pulsed PDC often poses a severe hindrance for the direct
implementation of the heralding of pure single-photon states or, for example,
continuous-variable entanglement distillation experiments. To get rid of
multimode effects narrowband frequency filtering is frequently applied to
achieve a single-mode behavior.
A rigorous theoretical description to accurately describe the effects of
filtering on PDC, however, is still missing. To date, the theoretical models of
filtered PDC are rooted in the discrete-variable domain and only account for
filtering in the low gain regime, where only a few photon pairs are emitted at
any single point in time. In this paper we extend these theoretical
descriptions and put forward a simple model, which is able to accurately
describe the effects of filtering on PDC in the continuous-variable domain.
This developed straightforward theoretical framework enables us to accurately
quantify the trade-off between suppression of higher-order modes, reduced
purity and lowered Einstein-Podolsky-Rosen (EPR) entanglement, when narrowband
filters are applied to multimode type-II PDC.Comment: 15 pages, 13 figure
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