Dimensionality Reduction Tool Research Articles

Guided optimization of ToxPi model weights using a Semi-Automated approach

The Toxicological Prioritization Index (ToxPi) is a visual analysis and decision support tool for dimension reduction and visualization of high throughput, multi-dimensional feature data. ToxPi was originally developed for assessing the relative toxicity of multiple chemicals or stressors by synthesizing complex toxicological data to provide a single comprehensive view of the potential health effects. It continues to be used for profiling chemicals and has since been applied to other types of “sample” entities, including geospatial (e.g. county-level Covid-19 risk and sites of historical PFAS exposure) and other profiling applications. For any set of features (data collected on a set of sample entities), ToxPi integrates the data into a set of weighted slices that provide a visual profile and a score metric for comparison. This scoring system is highly dependent on user-provided feature weights, yet users often lack knowledge of how to define these feature weights. Common methods for predicting feature weights are generally unusable due to inappropriate statistical assumptions and lack of global distributional expectation. However, users often have an inherent understanding of expected results for a small subset of samples. For example, in chemical toxicity, prior knowledge can often place subsets of chemicals into categories of low, moderate or high toxicity (reference chemicals). Ordinal regression can be used to predict weights based on these response levels that are applicable to the entire feature set, analogous to using positive and negative controls to contextualize an empirical distribution. We propose a semi-supervised method utilizing ordinal regression to predict a set of feature weights that produces the best fit for the known response (“reference”) data and subsequently fine-tunes the weights via a customized genetic algorithm. We conduct a simulation study to show when this method can improve the results of ordinal regression, allowing for accurate feature weight prediction and sample ranking in scenarios with minimal response data. To ground-truth the guided weight optimization, we test this method on published data to build a ToxPi model for comparison against expert-knowledge-driven weight assignments.

BinaryClust2: An Integrated Computational Pipeline for Systematic Mining of Mass Cytometry Data to Assist Deep Immune Profiling in Haematological Research

Introduction: The key role of immune system in modulating treatment efficacy and clinical outcomes in the settings of haematological diseases has been well recognized through the application of flow cytometry technologies over years. Mass cytometry (MC) is a next generation cytometry platform to simultaneously profile over 40 protein markers on single-cell resolution, which facilitates clinical research on immune monitoring and biomarker discovery. Nonetheless, the high-dimensional data generated present a daunting challenge for clinical investigators. Therefore, we describe BinaryClust2 (https://github.com/JingAnyaSun/BinaryClust2), an R-based computational framework integrated with the state-of-the-art algorithms and novel cell lineage characterisation method to assist comprehensive exploration of liquid MC data. Method: Here, we present the implementation of BinaryClust2 to three example MC datasets: In-house dataset from peripheral blood mononuclear cells (PBMCs) of 9 baseline myeloproliferative neoplasm (MPN) patients (~4 million cells), previously published data from 11 MPN patients receiving influenza vaccine (~0.2million cells), and published dataset of 59 covid patients and 23 healthy donors (~2million cells). BinaryClust2 has a streamlined analytical workflow, which comprises the following steps (Figure 1A): Step 1: Quality control, batch effect evaluation and correction Data quality control is a separate step before downstream analysis which includes diagnostic plots and batch effect examination. Algorithms CytofRUV and CytoNorm are available in the pipeline to remove unwanted variations caused by batch effects. Step 2: Semi-supervised identification of main cell types BinaryClust2 adopts a knowledge-based semi-supervised approach to predict main cell types. Users are required to provide a simple marker expression matrix of pre-defined cell types along with fcs files and metadata to construct a SingleCellExperiment (SCE) object, then the embedded algorithm can automatically classify cell populations without manual annotation. Step 3: In-depth interrogation and differential testing Specific population can be further extracted from whole cells and subject to in-depth exploration using unsupervised algorithms for subpopulation discovery. Dimensionality reduction tools UMAP and TSNE, unsupervised clustering methods Phenograph and flowSOM, and various data visualization plotting functions are offered in BinaryClust2. For statistical analysis, multiple study group comparison (n>2) of cell abundance and functional marker expression is supported via Kruskal Wallis test with multiple testing correction and post hoc analysis. Results: The performance of the semi-supervised classification function was tested independently in the MPN and influenza PBMC datasets, 7 main cell lineages were identified with accuracy comparable to manual gating by human experts (Figure 1B): average F-measure reached 0.93 and 0.98 respectively. Moreover, taking manual gating as ground truth reference, BinaryClust2 outperformed the unsupervised approach flowSOM concerning accuracy (F-measure: 0.93 vs. 0.70) and speed (140s vs 339s) in MPN dataset, while remaining equivalent to the well-performing semi-supervised approach LDA in accuracy (F-measure: 0.93 vs. 0.93) but faster in runtime (140s vs 595s), as shown in Table 1. Application to covid-19 dataset by Chevrier et al. achieved reproducible results and additional discoveries. 13 main cell types were characterised, abundance of B cells, Basophils, cDCs, DN T cells, Monocytes, Neutrophils, NK cells, pDCs, CD8 T cells obtained statistical significance (all P<0.05) among study conditions (healthy, mild covid, severe covid). We also grouped markers reflecting functional status of immune cells and found Granzyme B expression was significantly increased in the majority of main immune cells of covid patients. Phenograph was further applied in neutrophils and monocytes and returned 14 and 16 subsets respectively. Conclusion: Overall, BinaryClust2 incorporates expert's prior biological knowledge in a semi-supervised fashion to accurately deconvolute well-defined main cell lineages, while also preserving the potential of unsupervised approaches to discover novel cell subsets and providing a user-friendly toolset to remove the analytical barrier for high-dimensional immune profiling.

Similarity-assisted variational autoencoder for nonlinear dimension reduction with application to single-cell RNA sequencing data

BackgroundDeep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers. The variational autoencoder (VAE) is a popular deep generative method equipped with encoder/decoder structures. The encoder and decoder are useful when a new sample is mapped to the latent space and a data point is generated from a point in a latent space. However, the VAE tends not to show grouping pattern clearly without additional annotation information. On the other hand, similarity-based dimension reduction methods such as t-SNE or UMAP present clear grouping patterns even though these methods do not have encoder/decoder structures.ResultsTo bridge this gap, we propose a new approach that adopts similarity information in the VAE framework. In addition, for biological applications, we extend our approach to a conditional VAE to account for covariate effects in the dimension reduction step. In the simulation study and real single-cell RNA sequencing data analyses, our method shows great performance compared to existing state-of-the-art methods by producing clear grouping structures using an inferred encoder and decoder. Our method also successfully adjusts for covariate effects, resulting in more useful dimension reduction.ConclusionsOur method is able to produce clearer grouping patterns than those of other regularized VAE methods by utilizing similarity information encoded in the data via the highly celebrated UMAP loss function.

Neonatal Hypoxic-Ischemic Encephalopathy Grading from Multi-Channel EEG Time-Series Data Using a Fully Convolutional Neural Network

A deep learning classifier is proposed for grading hypoxic-ischemic encephalopathy (HIE) in neonates. Rather than using handcrafted features, this architecture can be fed with raw EEG. Fully convolutional layers were adopted both in the feature extraction and classification blocks, which makes this architecture simpler, and deeper, but with fewer parameters. Here, two large (335 h and 338 h, respectively) multi-center neonatal continuous EEG datasets were used for training and testing. The model was trained based on weak labels and channel independence. A majority vote method was used for the post-processing of the classifier results (across time and channels) to increase the robustness of the prediction. A dimension reduction tool, UMAP, was used to visualize the model classification effect. The proposed system achieved an accuracy of 86.09% (95% confidence interval: 82.41–89.78%), an MCC of 0.7691, and an AUC of 86.23% on the large unseen test set. Two convolutional neural network architectures which utilized time-frequency distribution features were selected as the baseline as they had been developed or tested on the same datasets. A relative improvement of 23.65% in test accuracy was obtained as compared with the best baseline. In addition, if only one channel was available, the test accuracy was only reduced by 2.63–5.91% compared with making decisions based on the eight channels.

Nonlinear dimensionality reduction methods for potentiometric multisensor systems data analysis

AbstractElectrochemical multisensor systems were proven to be a very perspective research direction in modern analytical chemistry. The multisensor approach assumes an employment of cross‐sensitive chemical sensors in combination with multivariate data processing methods. Dimensionality reduction of the data obtained from multisensor systems is a very important step and it is mostly based on the traditional tools of chemometrics, such as Principal Component Analysis (PCA). In case of chemically complex samples, the response of multisensor systems may have a complex nonlinear nature and the use of linear modelling methods does not seem optimal. However, the potential of nonlinear dimensionality reduction methods in the processing of multisensor data has not yet been systematically studied. In this report we aim to fill this gap and assess the performance of various nonlinear dimensionality reduction tools: Isomap, Self‐Organizing Kohonen Maps, and Autoencoder. These methods were explored using three datasets from potentiometric multisensor systems obtained in various real applications. It was shown that nonlinear dimensionality reduction methods give the possibility to obtain additional and more detailed information about the analyzed objects/processes compared to PCA. However, calculation time for nonlinear dimensionality reduction methods essentially exceeds that for PCA, and it can be a limiting factor for application of such algorithms.

Public Usage of E-Government in EU Countries: Are There Any Consequences for Tax Evasion?

Due to the processes of digitalization and automation, the e-Government has become an essential tool of public administration. The paper deals with the problem of e-Government usage by the public and its potential connection to tax evasion. The analysis is based on available secondary panel and cross-sectional data on the level of EU countries in the period 2008 to 2021. We compare the situation in the countries and classify them into homogenous clusters based on the overall public usage of e-Government. Principal component analysis and cluster analysis have been used as tools for dimension reduction and clustering. Moreover, we also found evidence of a potential relationship between the usage of e-Government and tax evasion. The provision of online information and services by the government to its citizens as well as online communication with public authorities are related to the lower level of tax evasion in the country. Hence, public authorities should support e-Government usage and e-filing systems to fight against tax evasion.

Analyzing Nexus between Economic Complexity, Renewable Energy, and Environmental Quality in Japan: A New Evidence from QARDL Approach

The economic complexity index is an effective dimensionality reduction tool that is applied to forecast and predict future economic growth, income, and environmental quality. Renewable energy plays an important role in mitigation of carbon dioxide emissions. This study explores the nexus between economic complexity, renewable energy, FDI, trade, and environmental quality in Japan for the period 1970Q1-2019Q4. We use carbon dioxide (CO2) emissions as dependent variable while economic complexity index (ECI), foreign direct investment (FDI) inflow, renewable energy (RNE), and trade as explanatory variables. This study applies a quantile autoaggressive approach for analysis; the result of this study suggests a long-run implication of the ECI, FDI, GDP, RNE, and trade for the CO2 emissions. While only RNE and trade show mixed results in the short run, the rest of the variables do not have short-run implications. This implies that emissions mostly result in the industrial production activities only in the long run and in some quantiles only in the short run. The Japanese government may adopt different measures to reduce the CO2 emissions in the country, such as carbon tax and tax exemption on renewable energy investment. Furthermore, the government may adopt the renewal energy in production, which could achieve sustainable development goal.

Convergence of mechanistic modeling and artificial intelligence in hydrologic science and engineering

Hydrology is a mature physical science based on application of first principles. However, the water system is complex and its study requires analysis of increasingly large data available from conventional and novel remote sensing and IoT sensor technologies. New data-driven approaches like Artificial Intelligence (AI) and Machine Learning (ML) are attracting much “hype” despite their apparent limitations (transparency, interpretability, ethics). Some AI/ML applications lack in addressing explicitly important hydrological questions, focusing mainly on “black-box” prediction without providing mechanistic insights. We present a typology of four main types of hydrological problems based on their dominant space and time scales, review their current tools and challenges, and identify important opportunities for AI/ML in hydrology around three main topics: data management, insights and knowledge extraction, and modelling structure. Instead of just for prediction, we propose that AI/ML can be a powerful inductive and exploratory dimension-reduction tool within the rich hydrological toolchest to support the development of new theories that address standing gaps in changing hydrological systems. AI/ML can incorporate other forms of structured and non-structured data and traditional knowledge typically not considered in process-based models. This can help us further advance process-based understanding, forecasting and management of hydrological systems, particularly at larger integrated system scales with big models. We call for reimagining the original definition of AI in hydrology to incorporate not only today’s main focus on learning, but on decision analytics and action rules, and on development of autonomous machines in a continuous cycle of learning and refinement in the context of strong ethical, legal, social, and economic constrains. For this, transdisciplinary communities of knowledge and practice will need to be forged with strong investment from the public sector and private engagement to protect water as a common good under accelerated demand and environmental change.

Supervised kernel principal component analysis for forecasting

Principal component analysis (PCA) is a versatile tool for dimension reduction with many applications in finance, economics, and machine learning. This paper proposes a new approach to improving the forecasting ability of the Principal Components (PCs) of observed high-dimensional predictors in a factor-augmented forecasting framework. The approach is carried out in a three-step procedure, where we first perform a nonparametric kernel regression of the target variable on each predictor to obtain a new high-dimensional predictor vector formed by stacking all estimated kernel regression functions, we then extract PCs from these new predictors using PCA, and finally, we employ the extracted PCs as predictors to forecast the target variable. A real example on macroeconomic forecasting is analyzed and numerical results show that the proposed kernel PCA can outperform some commonly used forecasting approaches in out-of-sample prediction.

Deep learning pipeline for quality filtering of MRSI spectra.

With the rise of novel 3D magnetic resonance spectroscopy imaging (MRSI) acquisition protocols in clinical practice, which are capable of capturing a large number of spectra from a subject's brain, there is a need for an automated preprocessing pipeline that filters out bad-quality spectra and identifies contaminated but salvageable spectra prior to the metabolite quantification step. This work introduces such a pipeline based on an ensemble of deep-learning classifiers. The dataset consists of 36,338 spectra from one healthy subject and five brain tumor patients, acquired with an EPSI variant, which implemented a novel type of spectral editing named SLOtboom-Weng (SLOW) editing on a 7T MR scanner. The spectra were labeled manually by an expert into four classes of spectral quality as follows: (i) noise, (ii) spectra greatly influenced by lipid-related artifacts (deemed not to contain clinical information), (iii) spectra containing metabolic information slightly contaminated by lipid signals, and (iv) good-quality spectra. The AI model consists of three pairs of networks, each comprising a convolutional autoencoder and a multilayer perceptron network. In the classification step, the encoding half of the autoencoder is kept as a dimensionality reduction tool, while the fully connected layers are added to its output. Each of the three pairs of networks is trained on different representations of spectra (real, imaginary, or both), aiming at robust decision-making. The final class is assigned via a majority voting scheme. The F1 scores obtained on the test dataset for the four previously defined classes are 0.96, 0.93, 0.82, and 0.90, respectively. The arguably lower value of 0.82 was reached for the least represented class of spectra mildly influenced by lipids. Not only does the proposed model minimise the required user interaction, but it also greatly reduces the computation time at the metabolite quantification step (by selecting a subset of spectra worth quantifying) and enforces the display of only clinically relevant information.

Principal weighted least square support vector machine: An online dimension-reduction tool for binary classification

As relevant technologies advance, streamed data are frequently encountered in various applications, and the need for scalable algorithms becomes urgent. In this article, we propose the principal weighted least square support vector machine (PWLSSVM) as a novel tool for SDR in binary classification where most SDR methods suffer since they assume continuous Y. We further show that the PWLSSVM can be employed for the online SDR for the streamed data. Namely, the PWLSSVM estimator can be directly updated from the new data without having old data. We explore the asymptotic properties of the PWLSSVM estimator and demonstrate its promising performance in terms of both estimation accuracy and computational efficiency for both simulated and real data.

EMBED: Essential MicroBiomE Dynamics, a dimensionality reduction approach for longitudinal microbiome studies

Dimensionality reduction offers unique insights into high-dimensional microbiome dynamics by leveraging collective abundance fluctuations of multiple bacteria driven by similar ecological perturbations. However, methods providing lower-dimensional representations of microbiome dynamics both at the community and individual taxa levels are not currently available. To that end, we present EMBED: Essential MicroBiomE Dynamics, a probabilistic nonlinear tensor factorization approach. Like normal mode analysis in structural biophysics, EMBED infers ecological normal modes (ECNs), which represent the unique orthogonal modes capturing the collective behavior of microbial communities. Using multiple real and synthetic datasets, we show that a very small number of ECNs can accurately approximate microbiome dynamics. Inferred ECNs reflect specific ecological behaviors, providing natural templates along which the dynamics of individual bacteria may be partitioned. Moreover, the multi-subject treatment in EMBED systematically identifies subject-specific and universal abundance dynamics that are not detected by traditional approaches. Collectively, these results highlight the utility of EMBED as a versatile dimensionality reduction tool for studies of microbiome dynamics.

Partial sufficient variable screening with categorical controls

Variable screening as a fast and effective dimension reduction tool plays an important role in analyzing ultrahigh dimensional data. While a very large number of actual datasets contain both continuous and categorical variables, existing methods are mostly designed for continuous data. Partial sufficient variable screening, which aims to reduce the predictive set of primary interest without loss of regression information in the presence of some control variables, is proposed with theoretical guarantees. Specifically, for regression analyses involving mixed types of predictors, variable screening is approached under the notion of sufficiency by constraining the reduction of the continuous variables through the subpopulations identified by the categorical variables. The effectiveness of the proposed method is demonstrated through simulation studies encompassing a variety of regression and classification models, and an application in prognostic gene screening for diffuse large-B-cell lymphoma.

FISHFactor: a probabilistic factor model for spatial transcriptomics data with subcellular resolution.

Factor analysis is a widely used tool for unsupervised dimensionality reduction of high-throughput datasets in molecular biology, with recently proposed extensions designed specifically for spatial transcriptomics data. However, these methods expect (count) matrices as data input and are therefore not directly applicable to single molecule resolution data, which are in the form of coordinate lists annotated with genes and provide insight into subcellular spatial expression patterns. To address this, we here propose FISHFactor, a probabilistic factor model that combines the benefits of spatial, non-negative factor analysis with a Poisson point process likelihood to explicitly model and account for the nature of single molecule resolution data. In addition, FISHFactor shares information across a potentially large number of cells in a common weight matrix, allowing consistent interpretation of factors across cells and yielding improved latent variable estimates. We compare FISHFactor to existing methods that rely on aggregating information through spatial binning and cannot combine information from multiple cells and show that our method leads to more accurate results on simulated data. We show that our method is scalable and can be readily applied to large datasets. Finally, we demonstrate on a real dataset that FISHFactor is able to identify major subcellular expression patterns and spatial gene clusters in a data-driven manner. The model implementation, data simulation and experiment scripts are available under https://www.github.com/bioFAM/FISHFactor.

State of the art in financial statement fraud detection: A systematic review

Over the past few decades, fraud has been increasingly prevalent, with large businesses like Satyam, Enron, and WorldCom making headlines for their deceptive financial reporting practices. In this research, we conducted a systematic review and bibliometric analysis of the literature concerning fraud detection in financial statements. Following a bibliometric analysis, we identified the leading researchers, publications, sources, countries, and collaboration patterns in financial statement fraud detection. Our systematic review covered the following topics: the data analytics tools used, databases used to identify fraudulent firms, the design of control group samples (non-fraudulent firms), the critical dimension reduction tools used, techniques adopted to address data rarity (imbalanced data), explanatory variables used in the model, theoretical framework supporting the fraud indicators, optimization techniques used, the use of evaluation metrics, and significant findings. The systematic review followed the approach provided by Tranfield et al. (2003), and the bibliometric analysis was conducted using the VOSviewer. Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA), 2020 reporting criteria were followed for reporting the systematic review's findings. We provide a brief overview of the existing literature, drawing both conclusions and recommendations for directions in which additional study is warranted. Our results provide valuable information that can be used by future academics, auditors, enforcement agencies, and regulators as they work to create the most effective fraud detection algorithms possible.

A molecular phenology scale of grape berry development.

Fruit growth and development consist of a continuous succession of physical, biochemical, and physiological changes driven by a genetic program that dynamically responds to environmental cues. Establishing recognizable stages over the whole fruit lifetime represents a fundamental requirement for research and fruit crop cultivation. This is especially relevant in perennial crops like grapevine (Vitis vinifera L.) to scale the development of its fruit across genotypes and growing conditions. In this work, molecular-based information from several grape berry transcriptomic datasets was exploited to build a molecular phenology scale (MPhS) and to map the ontogenic development of the fruit. The proposed statistical pipeline consisted of an unsupervised learning procedure yielding an innovative combination of semiparametric, smoothing, and dimensionality reduction tools. The transcriptomic distance between fruit samples was precisely quantified by means of the MPhS that also enabled to highlight the complex dynamics of the transcriptional program over berry development through the calculation of the rate of variation of MPhS stages by time. The MPhS allowed the alignment of time-series fruit samples proving to be a complementary method for mapping the progression of grape berry development with higher detail compared to classic time- or phenotype-based approaches.

A monotone single index model for missing-at-random longitudinal proportion data

Beta distributions are commonly used to model proportion valued response variables, often encountered in longitudinal studies. In this article, we develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using a interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilize Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat.

The influence of weather types over northern Greece on respiratory and cardio-vascular mortality

Extreme ambient temperatures are well-known for their adverse impact on public health, in the form of increased mortality and morbidity due to respiratory and cardio-vascular diseases. However, to capture the total impact of weather on cause-specific mortality/morbidity, the synoptic atmospheric conditions over the region under study need to be taken into account. The objective of this work is to identify weather types over Thessaloniki, Greece, statistically associated with mortality from circulatory and respiratory diseases, in an attempt to holistically determine the impact of weather on cause-specific mortality in the region. For this purpose, we employed datasets from the NCEP/NCAR Reanalysis comprising intrinsic daily data, gridded at a resolution of 2.5°×2.5° and covering a 41-year period (1980-2020). The first set used contains data of 500 hPa and 1,000 hPa geopotential heights for the main geographical domain of the Mediterranean region (30°N-45°N, 10°Ε-35°E). The second set comprises meteorological variables (2 m temperature, specific humidity, 2 m zonal and 2 m meridional wind and total cloud cover) for a geographical domain of north Greece (40.95°Ν, 22.50°Ε-26.25°E). We applied a combination of principal components analysis (PCA) as a dimensionality reduction tool and k-means cluster analysis (CA) in order to group days with homogeneous synoptic meteorological parameters. The derived weather types were statistically correlated with respiratory and mortality data for the time-period 1999-2018. It was concluded that the most fatal conditions for public health in Thessaloniki were associated with weather types bringing low/extremely low ambient temperature over north Greece.

Immune cell profiles and patient clustering in complex cases of interstitial lung disease

Interstitial lung disease comprises numerous clinical entities posing significant challenges towards a prompt and accurate diagnosis. Amongst the contributing factors are intricate pathophysiological mechanisms, an overlap between conditions, and interobserver disagreement. We developed a model for patient clustering offering an additional approach to such complex clinical cases. The model is based on surface phenotyping of over 40 markers on immune cells isolated from bronchoalveolar lavage in combination with clinical data. Based on the marker expression pattern we constructed an individual immune cell profile, then merged these to create a global profile encompassing various pathologies. The contribution of each participant to the global profile was assessed through dimensionality reduction tools and the ensuing similarity between samples was calculated. Our model enables two approaches. First, assessing the immune cell population landscape similarity between patients within a diagnostic group allows rapid identification of divergent profiles, which is particularly helpful for cases with uncertain diagnoses. Second, sample clustering is based exclusively on the calculated similarity of the immune cell profiles, thereby removing physician bias and relying on cellular nearest neighbors.

Prior Knowledge Guided Ultra-high Dimensional Variable Screening with Application to Neuroimaging Data.

Variable screening is a powerful and efficient tool for dimension reduction under ultrahigh dimensional settings. However, most existing methods overlook useful prior knowledge in specific applications. In this work, from a Bayesian modeling perspective, we develop a unified variable screening procedure for the linear regression model. We discuss different constructions of posterior mean screening (PMS) statistics to incorporate different types of prior knowledge according to specific applications. With non-informative prior specifications, PMS is equivalent to high-dimensional ordinary least-square projections (HOLP). We establish the screening consistency property for PMS with different types of prior knowledge. We show that PMS is robust to prior misspecifications; and when the prior knowledge provides correct information on summarizing the true parameter settings, PMS can substantially improve the selection accuracy compared to HOLP and other existing methods. We illustrate our method with extensive simulation studies and an analysis of neuroimaging data.