Estimation of Photometric Redshifts. I. Machine-learning Inference for Pan-STARRS1 Galaxies Using Neural Networks

We present a new machine-learning model for estimating photometric redshifts with improved accuracy for galaxies in Pan-STARRS1 data release 1. Depending on the estimation range of redshifts, this model based on neural networks can handle the difficulty for inferring photometric redshifts. Moreover, to reduce bias induced by the new model's ability to deal with estimation difficulty, it exploits the power of ensemble learning. We extensively examine the mapping between input features and target redshift spaces to which the model is validly applicable to discover the strength and weaknesses of the trained model. Because our trained model is well calibrated, our model produces reliable confidence information about objects with non-catastrophic estimation. While our model is highly accurate for most test examples residing in the input space, where training samples are densely populated, its accuracy quickly diminishes for sparse samples and unobserved objects (i.e., unseen samples) in training. We report that out-of-distribution (OOD) samples for our model contain both physically OOD objects (i.e., stars and quasars) and galaxies with observed properties not represented by training data. The code for our model is available at https://github.com/GooLee0123/MBRNN for other uses of the model and retraining the model with different data.

Least Squares Support Vector Machine Regression Based on Sparse Samples and Mixture Kernel Learning

Least squares support vector machine (LSSVM) is a machine learning algorithm based on statistical theory. Itsadvantages include robustness and calculation simplicity, and it has good performance in the data processingof small samples. The LSSVM model lacks sparsity and is unable to handle large-scale data problem, this articleproposes an LSSVM method based on mixture kernel learning and sparse samples. This algorithm reduces theinitial training set to a sub-dataset using a sparse selection strategy. It converts the single kernel function in theLSSVM model into a mixed kernel function and optimizes its parameters. The reduced sub-dataset is used fortraining LSSVM. Finally, a group of datasets in the UCI Machine Learning Repository were used to verify theeffectiveness of the proposed algorithm, which is applied to real-world power load data to achieve better fittingand improve the prediction accuracy.

baredSC: Bayesian Approach to Retrieve Expression Distribution of Single-Cell

The number of studies using single-cell RNA sequencing (scRNA-seq) is constantly growing. This powerful technique provides a sampling of the whole transcriptome of a cell. However, the commonly used droplet-based method often produces very sparse samples. Sparsity can be a major hurdle when studying the distribution of the expression of a specific gene or the correlation between the expressions of two genes. We show that the main technical noise associated with these scRNA-seq experiments is due to the sampling (i.e. Poisson noise). We developed a new tool named baredSC, for Bayesian Approach to Retrieve Expression Distribution of Single-Cell, which infers the intrinsic expression distribution in noisy single-cell data using a Gaussian mixture model (GMM). baredSC can be used to obtain the distribution in one dimension for individual genes and in two dimensions for pairs of genes, in particular to estimate the correlation in the two genes' expressions. We apply baredSC to simulated scRNA-seq data and show that the algorithm is able to uncover the expression distribution used to simulate the data, even in multi-modal cases with very sparse data. We also apply baredSC to two real biological data sets. First, we use it to measure the anti-correlation between Hoxd13 and Hoxa11, two genes with known genetic interaction in embryonic limb. Then, we study the expression of Pitx1 in embryonic hindlimb, for which a trimodal distribution has been identified through flow cytometry. While other methods to analyze scRNA-seq are too sensitive to sampling noise, baredSC reveals this trimodal distribution.

Cosmological cross-correlations and nearest neighbour distributions

ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

Compressing H2 Matrices for Translationally Invariant Kernels

H2 matrices provide compressed representations of the matrices obtained when discretizing surface and volume integral equations. The memory costs associated with storing H2 matrices for static and low-frequency applications are O(N). However, when the H2 representation is constructed using sparse samples of the underlying matrix, the translation matrices in the H2 representation do not preserve any translational invariance present in the underlying kernel. In some cases, this can result in an H2 representation with relatively large memory requirements. This paper outlines a method to compress an existing H2 matrix by constructing a translationally invariant H2 matrix from it. Numerical examples demonstrate that the resulting representation can provide significant memory savings.

Nanometric axial localization of single fluorescent molecules with modulated excitation

Strategies have been developed in LIDAR to perform distance measurements for non-coherent emission in sparse samples based on excitation modulation. Super-resolution fluorescence microscopy is also striving to perform axial localization but through entirely different approaches. Here we revisit the amplitude modulated LIDAR approach to reach nanometric localization precision and we successfully adapt it to bring distinct advantages to super-resolution microscopy. The excitation pattern is performed by interference enabling the decoupling between spatial and time modulation. The localization of a single emitter is performed by measuring the relative phase of its linear fluorescent response to the known shifting excitation field. Taking advantage of a tilted interfering configuration, we obtain a typical axial localization precision of 7.5 nm over the entire field of view and the axial capture range, without compromising on the acquisition time, the emitter density or the lateral localization precision. The interfering pattern being robust to optical aberrations, this modulated localization (ModLoc) strategy is particularly well suited for observations deep in the samples. Images performed on various biological samples show that the localization precision remains nearly constant up to several micrometers.