arXiv subjects

William J. Welch

Publications and source records attributed to William J. Welch.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Optimization in Linear Time

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.

cs.LG↗

arXiv2025

A Gaussian Sliding Windows Regression Model for Hydrological Inference

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes in streamflow is of high practical importance. Since water can take a variety of flow paths to generate streamflow, a series of distinct runoff pulses may combine to create the observed streamflow time series. Current state-of-the-art models are not able to sufficiently confront the problem complexity with interpretable parametrization, thus preventing novel insights about the dynamics of distinct flow paths from being formed. The proposed Gaussian Sliding Windows Regression Model targets this problem by combining the concept of multiple windows sliding along the time axis with multiple linear regression. The window kernels, which indicate the weights applied to different time lags, are implemented via Gaussian-shaped kernels. As a result, straightforward process inference can be achieved since each window can represent one flow path. Experiments on simulated and real-world scenarios underline that the proposed model achieves accurate parameter estimates and competitive predictive performance, while fostering explainable and interpretable hydrological modeling.

stat.ME↗

arXiv2024

Learning from limited temporal data: Dynamically sparse historical functional linear models with applications to Earth science

Scientists and statisticians often want to learn about the complex relationships that connect two time-varying variables. Recent work on sparse functional historical linear models confirms that they are promising for this purpose, but several notable limitations exist. Most importantly, previous works have imposed sparsity on the historical coefficient function, but have not allowed the sparsity, hence lag, to vary with time. We simplify the framework of sparse functional historical linear models by using a rectangular coefficient structure along with Whittaker smoothing, then reduce the assumptions of the previous frameworks by estimating the dynamic time lag from a hierarchical coefficient structure. We motivate our study by aiming to extract the physical rainfall-runoff processes hidden within hydrological data. We show the promise and accuracy of our method using eight simulation studies, further justified by two real sets of hydrological data.

stat.ME↗

arXiv2023

Data-Adaptive Dimensional Analysis for Accurate Interpolation and Extrapolation in Computer Experiments

Dimensional analysis (DA) pays attention to fundamental physical dimensions such as length and mass when modelling scientific and engineering systems. It goes back at least a century to Buckingham's Pi theorem, which characterizes a scientifically meaningful model in terms of a limited number of dimensionless variables. The methodology has only been exploited relatively recently by statisticians for design and analysis of experiments, however, and computer experiments in particular. The basic idea is to build models in terms of new dimensionless quantities derived from the original input and output variables. A scientifically valid formulation has the potential for improved prediction accuracy in principle, but the implementation of DA is far from straightforward. There can be a combinatorial number of possible models satisfying the conditions of the theory. Empirical approaches for finding effective derived variables will be described, and improvements in prediction accuracy will be demonstrated. As DA's dimensionless quantities for a statistical model typically compare the original variables rather than use their absolute magnitudes, DA is less dependent on the choice of experimental ranges in the training data. Hence, we are also able to illustrate sustained accuracy gains even when extrapolating substantially outside the training data.

cs.LG↗

arXiv2023

Continuous Conditional Generative Adversarial Networks: Novel Empirical Losses and Label Input Mechanisms

This work proposes the continuous conditional generative adversarial network (CcGAN), the first generative model for image generation conditional on continuous, scalar conditions (termed regression labels). Existing conditional GANs (cGANs) are mainly designed for categorical conditions (eg, class labels); conditioning on regression labels is mathematically distinct and raises two fundamental problems:(P1) Since there may be very few (even zero) real images for some regression labels, minimizing existing empirical versions of cGAN losses (aka empirical cGAN losses) often fails in practice;(P2) Since regression labels are scalar and infinitely many, conventional label input methods are not applicable. The proposed CcGAN solves the above problems, respectively, by (S1) reformulating existing empirical cGAN losses to be appropriate for the continuous scenario; and (S2) proposing a naive label input (NLI) method and an improved label input (ILI) method to incorporate regression labels into the generator and the discriminator. The reformulation in (S1) leads to two novel empirical discriminator losses, termed the hard vicinal discriminator loss (HVDL) and the soft vicinal discriminator loss (SVDL) respectively, and a novel empirical generator loss. The error bounds of a discriminator trained with HVDL and SVDL are derived under mild assumptions in this work. Two new benchmark datasets (RC-49 and Cell-200) and a novel evaluation metric (Sliding Fréchet Inception Distance) are also proposed for this continuous scenario. Our experiments on the Circular 2-D Gaussians, RC-49, UTKFace, Cell-200, and Steering Angle datasets show that CcGAN is able to generate diverse, high-quality samples from the image distribution conditional on a given regression label. Moreover, in these experiments, CcGAN substantially outperforms cGAN both visually and quantitatively.

cs.CV↗

arXiv2022

Distilling and Transferring Knowledge via cGAN-generated Samples for Image Classification and Regression

Knowledge distillation (KD) has been actively studied for image classification tasks in deep learning, aiming to improve the performance of a student based on the knowledge from a teacher. However, applying KD in image regression with a scalar response variable has been rarely studied, and there exists no KD method applicable to both classification and regression tasks yet. Moreover, existing KD methods often require a practitioner to carefully select or adjust the teacher and student architectures, making these methods less flexible in practice. To address the above problems in a unified way, we propose a comprehensive KD framework based on cGANs, termed cGAN-KD. Fundamentally different from existing KD methods, cGAN-KD distills and transfers knowledge from a teacher model to a student model via cGAN-generated samples. This novel mechanism makes cGAN-KD suitable for both classification and regression tasks, compatible with other KD methods, and insensitive to the teacher and student architectures. An error bound for a student model trained in the cGAN-KD framework is derived in this work, providing a theory for why cGAN-KD is effective as well as guiding the practical implementation of cGAN-KD. Extensive experiments on CIFAR-100 and ImageNet-100 show that we can combine state of the art KD methods with the cGAN-KD framework to yield a new state of the art. Moreover, experiments on Steering Angle and UTKFace demonstrate the effectiveness of cGAN-KD in image regression tasks, where existing KD methods are inapplicable.

cs.CV↗

arXiv2022

Efficient Subsampling of Realistic Images From GANs Conditional on a Class or a Continuous Variable

Recently, subsampling or refining images generated from unconditional GANs has been actively studied to improve the overall image quality. Unfortunately, these methods are often observed less effective or inefficient in handling conditional GANs (cGANs) -- conditioning on a class (aka class-conditional GANs) or a continuous variable (aka continuous cGANs or CcGANs). In this work, we introduce an effective and efficient subsampling scheme, named conditional density ratio-guided rejection sampling (cDR-RS), to sample high-quality images from cGANs. Specifically, we first develop a novel conditional density ratio estimation method, termed cDRE-F-cSP, by proposing the conditional Softplus (cSP) loss and an improved feature extraction mechanism. We then derive the error bound of a density ratio model trained with the cSP loss. Finally, we accept or reject a fake image in terms of its estimated conditional density ratio. A filtering scheme is also developed to increase fake images' label consistency without losing diversity when sampling from CcGANs. We extensively test the effectiveness and efficiency of cDR-RS in sampling from both class-conditional GANs and CcGANs on five benchmark datasets. When sampling from class-conditional GANs, cDR-RS outperforms modern state-of-the-art methods by a large margin (except DRE-F-SP+RS) in terms of effectiveness. Although the effectiveness of cDR-RS is often comparable to that of DRE-F-SP+RS, cDR-RS is substantially more efficient. When sampling from CcGANs, the superiority of cDR-RS is even more noticeable in terms of both effectiveness and efficiency. Notably, with the consumption of reasonable computational resources, cDR-RS can substantially reduce Label Score without decreasing the diversity of CcGAN-generated images, while other methods often need to trade much diversity for slightly improved Label Score.

cs.CV↗

arXiv2020

Classification Beats Regression: Counting of Cells from Greyscale Microscopic Images based on Annotation-free Training Samples

Modern methods often formulate the counting of cells from microscopic images as a regression problem and more or less rely on expensive, manually annotated training images (e.g., dot annotations indicating the centroids of cells or segmentation masks identifying the contours of cells). This work proposes a supervised learning framework based on classification-oriented convolutional neural networks (CNNs) to count cells from greyscale microscopic images without using annotated training images. In this framework, we formulate the cell counting task as an image classification problem, where the cell counts are taken as class labels. This formulation has its limitation when some cell counts in the test stage do not appear in the training data. Moreover, the ordinal relation among cell counts is not utilized. To deal with these limitations, we propose a simple but effective data augmentation (DA) method to synthesize images for the unseen cell counts. We also introduce an ensemble method, which can not only moderate the influence of unseen cell counts but also utilize the ordinal information to improve the prediction accuracy. This framework outperforms many modern cell counting methods and won the data analysis competition (Case Study 1: Counting Cells From Microscopic Images https://ssc.ca/en/case-study/case-study-1-counting-cells-microscopic-images) of the 47th Annual Meeting of the Statistical Society of Canada (SSC). Our code is available at https://github.com/anno2020/CellCount_TinyBBBC005.

eess.IV↗

arXiv2020

Subsampling Generative Adversarial Networks: Density Ratio Estimation in Feature Space with Softplus Loss

Filtering out unrealistic images from trained generative adversarial networks (GANs) has attracted considerable attention recently. Two density ratio based subsampling methods---Discriminator Rejection Sampling (DRS) and Metropolis-Hastings GAN (MH-GAN)---were recently proposed, and their effectiveness in improving GANs was demonstrated on multiple datasets. However, DRS and MH-GAN are based on discriminator based density ratio estimation (DRE) methods, so they may not work well if the discriminator in the trained GAN is far from optimal. Moreover, they do not apply to some GANs (e.g., MMD-GAN). In this paper, we propose a novel Softplus (SP) loss for DRE. Based on it, we develop a sample-based DRE method in a feature space learned by a specially designed and pre-trained ResNet-34 (DRE-F-SP). We derive the rate of convergence of a density ratio model trained under the SP loss. Then, we propose three different density ratio subsampling methods (DRE-F-SP+RS, DRE-F-SP+MH, and DRE-F-SP+SIR) for GANs based on DRE-F-SP. Our subsampling methods do not rely on the optimality of the discriminator and are suitable for all types of GANs. We empirically show our subsampling approach can substantially outperform DRS and MH-GAN on a synthetic dataset and the CIFAR-10 dataset, using multiple GANs.

cs.LG↗

arXiv2019

Sequential Computer Experimental Design for Estimating an Extreme Probability or Quantile

A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead, we build a statistical surrogate for the input-output relationship with a modest number of evaluations and then sequentially add further runs, guided by a criterion to improve the estimate. We compare two criteria in the literature. Moreover, we investigate two practical questions: how to design the initial code runs and how to model the input distribution. Hence, we close the gap between the theory of sequential design and its application.

stat.ML↗

arXiv2019

Adaptive Partitioning Design and Analysis for Emulation of a Complex Computer Code

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the model. Historically, Gaussian process regression has proven to be the almost ubiquitous choice for a fast statistical emulator for such a computer model, due to its flexible form and analytical expressions for measures of predictive uncertainty. However, even this statistical emulator can be computationally intractable for large designs, due to computing time increasing with the cube of the design size. Multiple methods have been proposed for addressing this problem. We discuss several of them, and compare their predictive and computational performance in several scenarios. We then propose solving this problem using an adaptive partitioning emulator (APE). The new approach is motivated by the idea that most computer models are only complex in particular regions of the input space. By taking a data-adaptive approach to the development of a design, and choosing to partition the space in the regions of highest variability, we obtain a higher density of points in these regions and hence accurate prediction.

stat.ME↗

arXiv2018

Bayesian Optimization Using Monotonicity Information and Its Application in Machine Learning Hyperparameter

We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as monotonic functions of the hyperparameters. Our proposed algorithm adapts Bayesian optimization methods to incorporate the monotonicity constraints. We illustrate the advantages of exploiting monotonicity using illustrative examples and demonstrate the improvements in optimization efficiency for some machine learning hyperparameter tuning applications.

cs.LG↗

arXiv2017

Regression Phalanxes

Tomal et al. (2015) introduced the notion of "phalanxes" in the context of rare-class detection in two-class classification problems. A phalanx is a subset of features that work well for classification tasks. In this paper, we propose a different class of phalanxes for application in regression settings. We define a "Regression Phalanx" - a subset of features that work well together for prediction. We propose a novel algorithm which automatically chooses Regression Phalanxes from high-dimensional data sets using hierarchical clustering and builds a prediction model for each phalanx for further ensembling. Through extensive simulation studies and several real-life applications in various areas (including drug discovery, chemical analysis of spectra data, microarray analysis and climate projections) we show that an ensemble of Regression Phalanxes improves prediction accuracy when combined with effective prediction methods like Lasso or Random Forests.

stat.ML↗

arXiv2015

Resolving Protoplanetary Disks at Millimeter Wavelengths by CARMA

We present continuum observations at 1.3 and 2.7 mm using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) toward six protoplanetary disks in the Taurus molecular cloud: CI Tau, DL Tau, DO Tau, FT Tau, Haro 6-13, and HL Tau. We constrain physical properties of the disks with Bayesian inference using two disk models; flared power-law disk model and flared accretion disk model. Comparing the physical properties, we find that the more extended disks are less flared and that the dust opacity spectral index (beta) is smaller in the less massive disks. In addition, disks with a steeper mid-plane density gradient have a smaller beta, which suggests that grains grow and radially move. Furthermore, we compare the two disk models quantitatively and find that the accretion disk model provides a better fit overall. We also discuss the possibilities of substructures on three extended protoplanetary disks.

astro-ph.SR↗

arXiv2015

Ensembling classification models based on phalanxes of variables with applications in drug discovery

Statistical detection of a rare class of objects in a two-class classification problem can pose several challenges. Because the class of interest is rare in the training data, there is relatively little information in the known class response labels for model building. At the same time the available explanatory variables are often moderately high dimensional. In the four assays of our drug-discovery application, compounds are active or not against a specific biological target, such as lung cancer tumor cells, and active compounds are rare. Several sets of chemical descriptor variables from computational chemistry are available to classify the active versus inactive class; each can have up to thousands of variables characterizing molecular structure of the compounds. The statistical challenge is to make use of the richness of the explanatory variables in the presence of scant response information. Our algorithm divides the explanatory variables into subsets adaptively and passes each subset to a base classifier. The various base classifiers are then ensembled to produce one model to rank new objects by their estimated probabilities of belonging to the rare class of interest. The essence of the algorithm is to choose the subsets such that variables in the same group work well together; we call such groups phalanxes.

stat.ML↗

arXiv2012

Efficient, adaptive cross-validation for tuning and comparing models, with application to drug discovery

Cross-validation (CV) is widely used for tuning a model with respect to user-selected parameters and for selecting a "best" model. For example, the method of $k$-nearest neighbors requires the user to choose $k$, the number of neighbors, and a neural network has several tuning parameters controlling the network complexity. Once such parameters are optimized for a particular data set, the next step is often to compare the various optimized models and choose the method with the best predictive performance. Both tuning and model selection boil down to comparing models, either across different values of the tuning parameters or across different classes of statistical models and/or sets of explanatory variables. For multiple large sets of data, like the PubChem drug discovery cheminformatics data which motivated this work, reliable CV comparisons are computationally demanding, or even infeasible. In this paper we develop an efficient sequential methodology for model comparison based on CV. It also takes into account the randomness in CV. The number of models is reduced via an adaptive, multiplicity-adjusted sequential algorithm, where poor performers are quickly eliminated. By exploiting matching of individual observations, it is sometimes even possible to establish the statistically significant inferiority of some models with just one execution of CV.

stat.AP↗

arXiv2005

A High-Mass Protobinary System in the Hot Core W3(H2O)

We have observed a high-mass protobinary system in the hot core W3(H2O) with the BIMA Array. Our continuum maps at wavelengths of 1.4mm and 2.8mm both achieve sub-arcsecond angular resolutions and show a double-peaked morphology. The angular separation of the two sources is 1.19" corresponding to 2.43X10^3 AU at the source distance of 2.04 kpc. The flux densities of the two sources at 1.4mm and 2.8mm have a spectral index of 3, translating to an opacity law of kappa ~ nu. The small spectral indices suggest that grain growth has begun in the hot core. We have also observed 5 K components of the CH3CN (12-11) transitions. A radial velocity difference of 2.81 km/s is found towards the two continuum peaks. Interpreting these two sources as binary components in orbit about one another, we find a minimum mass of 22 Msun for the system. Radiative transfer models are constructed to explain both the continuum and methyl cyanide line observations of each source. Power-law distributions of both density and temperature are derived. Density distributions close to the free-fall value, r^-1.5, are found for both components, suggesting continuing accretion. The derived luminosities suggest the two sources have equivalent zero-age main sequence (ZAMS) spectral type B0.5 - B0. The nebular masses derived from the continuum observations are about 5 Msun for source A and 4 Msun for source C. A velocity gradient previously detected may be explained by unresolved binary rotation with a small velocity difference.

astro-ph↗

arXiv2005

Far-Infrared and Millimeter Continuum Studies of K Giants: Alpha Boo and Alpha Tau

We have imaged two normal, non-coronal, infrared-bright K giants, Alpha Tau and Alpha Boo, in the 1.4-mm and 2.8-mm continuum using the Berkeley Illinois Maryland Association millimeter array. These stars have been used as important absolute calibrators for several infrared infrared satellites. Our goals are: (1) to establish whether these stars radiate as simple photospheres or possess long-wavelength chromospheres; and (2) to make a connection between millimeter wave and far-infrared absolute flux calibrations. To accomplish these goals we also present Infrared Space Observatory Long Wavelength Spectrometer measurements of both these K giants. The far-infrared and millimeter continuum radiation is produced in the vicinity of the temperature minimum in Alpha Tau and Alpha Boo. We find that current photospheric models predict fluxes in reasonable agreement with those observed for wavelengths which sample the upper photosphere, namely <=125 microns in Alpha Tau and Alpha Boo. We clearly detect chromospheric radiation from both stars by 2.8mm (by 1.4mm in the case of Alpha Boo). Only additional observations can determine precisely where beyond 125 microns the purely radiative models fail. Until then, purely radiative models for these stars can only be used with confidence for calibration purposes below 125 microns.

astro-ph↗