Pairwise Modeling Research Articles

Measuring the significance of higher-order dependency in networks

Higher-order networks (HONs), which go beyond the limitations of pairwise relation modeling by graphs, capture higher-order dependencies involving three or more components for various systems. As the number of potential higher-order dependencies increases exponentially with both network size and the order of dependency, it is of particular importance for HON models to balance their representation power against model complexity. In this study, we propose a method, significant k-order dependencies mining (SkDM), based on hypothesis testing and the Markov chain Monte Carlo (MCMC), to identify significant higher-order dependencies in real systems. Through synthetic clickstreams with elaborately designed higher-order dependencies, SkDM shows a powerful ability to correctly identify all significant dependencies at preset significance levels of α={0}{.01, 0}{.05, 0}{.10} , performing as the only method, in comparison to the state of the arts, that can robustly maintain the Type I error rate, and without generating any Type II error across all the experimental settings. We further apply the SkDM method to various empirical networks, including journal citations, air traffic, and email communications. Empirical results show that among those tested networks, only 6.03%, 1.47%, and 1.28% of all potential dependencies are of statistical significance ( α={0}{.01} ). The proposed SkDM method, therefore, provides an efficient tool for higher-order network analysis tasks at reduced computational complexity.

Corpora amylacea negatively correlate with hippocampal tau pathology in Alzheimer's disease.

Severity and distribution of aggregated tau and neurofibrillary tangles (NFT) are strongly correlated with the clinical presentation of Alzheimer's disease (AD). Clearance of aggregated tau could decrease the rate of NFT formation and delay AD onset. Recent studies implicate corpora amylacea (CA) as a regulator of onset or accumulation of tau pathology. Normally, CA clear brain waste products by amassing cellular debris, which are then extruded into the cerebrospinal fluid to be phagocytosed. The proper functioning of CA may slow progression of AD-associated NFT pathology, and this relationship may be influenced by amount and distribution of phospho-tau (pTau) produced, age, sex, and genetic risk. The goal of this study was to determine if CA size and number are associated with hippocampal location and local pTau severity while accounting for variations in age, sex, and genetic risk. Postmortem brain hippocampal tissue sections from 40 AD and 38 unaffected donors were immunohistochemically stained with AT8 (pTau) and counter stained with periodic acid Schiff (PAS). Stained sections of the CA1 and CA3 regions of the hippocampus were analyzed. The percent area occupied (%AO) of CA, pTau, and NFT was calculated. Pairwise comparisons and regression modeling were used to analyze the influence of age, pTau %AO, and genetic risk on %AO by CA in each region, separately in donors with AD and unaffected donors. CA %AO was significantly higher in the CA3 region compared to CA1 in both groups. A significant negative correlation of CA %AO with both pTau %AO and neurofibrillary tangle %AO in the CA3 region of AD brain donors was found. Regression analysis in the CA3 region revealed a significant negative association between CA with both pTau and age. We found an increase of CA in the CA3 region, compared to CA1 region, in AD and unaffected donors. This may suggest that the CA3 region is a hub for waste removal. Additionally, the negative correlation between %AO by CA and NFT in the CA3 region of the hippocampus in donors with AD suggests CA could play a role in AD pathologic progression by influencing tau clearance.

Metabolic model-based ecological modeling for probiotic design.

The microbial community composition in the human gut has a profound effect on human health. This observation has lead to extensive use of microbiome therapies, including over-the-counter 'probiotic' treatments intended to alter the composition of the microbiome. Despite so much promise and commercial interest, the factors that contribute to the success or failure of microbiome-targeted treatments remain unclear. We investigate the biotic interactions that lead to successful engraftment of a novel bacterial strain introduced to the microbiome as in probiotic treatments. We use pairwise genome-scale metabolic modeling with a generalized resource allocation constraint to build a network of interactions between taxa that appear in an experimental engraftment study. We create induced sub-graphs using the taxa present in individual samples and assess the likelihood of invader engraftment based on network structure. To do so, we use a generalized Lotka-Volterra model, which we show has strong ability to predict if a particular invader or probiotic will successfully engraft into an individual's microbiome. Furthermore, we show that the mechanistic nature of the model is useful for revealing which microbe-microbe interactions potentially drive engraftment.

Changes of anthocyanin and amino acid metabolites in saffron petals (Crocus sativus L.) during fermentation based on untargeted metabolomics

In order to investigate the possibility of fermentation for deep processing of saffron petals, the metabolic profiles of anthocyanins and amino acids in saffron petals were studied by untargeted metabolomics method based on ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS) combined with multivariate statistical analysis. The PCA, OPLS-DA and HCA models were established to analyze the differential metabolites before and after fermentation. Subsequently, the differential metabolites were screened by OPLS-DA with pairwise modeling. The contents of 26 kinds of anthocyanins during fermentation and 23 kinds of anthocyanins after fermentation were significantly different, respectively. After fermentation, the total anthocyanin content increased, and the monomer anthocyanin produced a variety of glucoside anthocyanin. As for amino acid metabolism, there were significant differences in 24 amino acids during fermentation, 27 kinds of amino acids after fermentation, and then the total content of amino acids decreased. In addition, based on the KEEG database, several metabolic pathways during the fermentation process were identified, and the metabolism pathway of anthocyanin is primarily related to anthocyanin biosynthesis, while the metabolic pathway of amino acid is mainly related to metabolic pathways. These findings provide comprehensive insights into the quality improvements of saffron petals wine.

Choice of fractionation regimen for Grade IV gliomas depending on rapid early progression

To investigate the effect of two fractionation regimens on survival in patients with Grade IV gliomas depending on rapid early progression (REP). Fractionation with prescribed doses of 2 and 3 Gy was alternately used in 140 patients with morphologically confirmed Grade IV glioma using a pairwise modeling strategy. REP was diagnosed in 60 (42.9%) out of 140 patients with Grade IV gliomas and 55 (45.5%) out of 121 patients with glioblastomas. Fatal outcome was observed in 111 (79.3%) patients, 99 (70.7%) ones died from progression of glioma. In case of no REP, the median overall survival as of December 2023 was 32.20 (95% CI 25.7-38.7) months, with REP - only 16.03 (95% CI 13.5-18.6) months (p<0.0001). Median survival was slightly lower in patients with glioblastoma - 28.2 and 16.5 months, respectively (p<0.0001). In patients with Grade IV gliomas and no REP, 3 Gy fractionation regimen has significant advantages over standard radiotherapy regarding overall survival. In case of more aggressive course of tumor (REP), higher single dose does not improve treatment outcomes. Isoeffective dose ≥59.5Gy is of great importance.

Выбор режима фракционирования при глиомах 4 степени злокачественности в зависимости от возраста пациентов

The aim of the work is to study the effect of two dose fractionation regimens on subsequent survival in patients with grade 4 gliomas, depending on age. In 140 patients with morphologically confirmed grade 4 glioma, fractionation with the prescribed dose of 2 and 3 Gy was alternately used using a pairwise modeling strategy. Of these, 111 patients (79.3%) died, 99 (70.7%) from glioma progression. In the group &lt;50 years old, the median overall survival as of December 2023 was 31.11 months (95% Cl: 21.0-41.2), ≥50 years – 18.99 months (95% Cl: 16.0-21.0; p=0.014). In the group ≥50 years old with the fractionation mode of 3 Gy, the median overall survival was 21.32 months (n=47; 95% Cl: 12.1-30.6), with the mode of 2 Gy – 16.29 months (n=47; 95% Cl: 12.3-20.3; p=0.037). With glioblastoma, there are no statistical differences between the two irradiation programs – the medians are 20.0 and 16.4 months, respectively (p=0.118). In the group &lt;50 years old with the fractionation mode of 3 Gy, the median overall survival was 32.49 months (n=23; 95% Cl: 7.1-57.9), with the mode of 2 Gy – 29.11 months (n=23; 95% Cl: 17.6-40.6; p=0.717). With glioblastoma, there are no statistical differences between the two radiotherapy programs – the median is 18.3 and 23.7 months, respectively (p=0.710). The data obtained indicate the expediency of using hypofractive radiotherapy regimens for grade 4 gliomas in patients over 50 years of age, radiation therapy should be carried out with a sufficiently high dose level, including in patients over 70 years of age with good functional condition. In young patients, approaches with increasing single doses do not lead to improved results. The fractionation regimen with a dose of 2 Gy should be considered optimal for radiation therapy.

Statistical Modeling of Implicit Functional Relations

This study considers the statistical estimation of relations presented by implicit functions. Such structures define mutual interconnections of variables rather than outcome variable dependence by predictor variables considered in regular regression analysis. For a simple case of two variables, pairwise regression modeling produces two different lines of each variable dependence using another variable, but building an implicit relation yields one invertible model composed of two simple regressions. Modeling an implicit linear relation for multiple variables can be expressed as a generalized eigenproblem of the covariance matrix of the variables in the metric of the covariance matrix of their errors. For unknown errors, this work describes their estimation by the residual errors of each variable in its regression by the other predictors. Then, the generalized eigenproblem can be reduced to the diagonalization of a special matrix built from the variables’ covariance matrix and its inversion. Numerical examples demonstrate the eigenvector solution’s good properties for building a unique equation of the relations between all variables. The proposed approach can be useful in practical regression modeling with all variables containing unobserved errors, which is a common situation for the applied problems.

Learning to Select from Multiple Options

Many NLP tasks can be regarded as a selection problem from a set of options, such as classification tasks, multi-choice question answering, etc. Textual entailment (TE) has been shown as the state-of-the-art (SOTA) approach to dealing with those selection problems. TE treats input texts as premises (P), options as hypotheses (H), then handles the selection problem by modeling (P, H) pairwise. Two limitations: first, the pairwise modeling is unaware of other options, which is less intuitive since humans often determine the best options by comparing competing candidates; second, the inference process of pairwise TE is time-consuming, especially when the option space is large. To deal with the two issues, this work first proposes a contextualized TE model (Context-TE) by appending other k options as the context of the current (P, H) modeling. Context-TE is able to learn more reliable decision for the H since it considers various context. Second, we speed up Context-TE by coming up with Parallel-TE, which learns the decisions of multiple options simultaneously. Parallel-TE significantly improves the inference speed while keeping comparable performance with Context-TE. Our methods are evaluated on three tasks (ultra-fine entity typing, intent detection and multi-choice QA) that are typical selection problems with different sizes of options. Experiments show our models set new SOTA performance; particularly, Parallel-TE is faster than the pairwise TE by k times in inference.

Saliency Map Estimation Using a Pixel-Pairwise-Based Unsupervised Markov Random Field Model

This work presents a Bayesian statistical approach to the saliency map estimation problem. More specifically, we formalize the saliency map estimation issue in the fully automatic Markovian framework. The major and original contribution of the proposed Bayesian–Markov model resides in the exploitation of a pixel pairwise modeling and a likelihood model based on a parametric mixture of two different class-conditional likelihood distributions whose parameters are adaptively and previously estimated for each image. This allows us to adapt our saliency estimation model to the specific characteristics of each image of the dataset and to provide a nearly parameter-free—hence dataset-independent—unsupervised saliency map estimation procedure. In our case, the parameters of the likelihood model are all estimated under the principles of the iterative conditional estimation framework. Once the estimation step is completed, the MPM (maximum posterior marginal) solution of the saliency map (which we show as particularly suitable for this type of estimation), is then estimated by a stochastic sampling scheme approximating the posterior distribution (whose parameters were previously estimated). This unsupervised data-driven Markovian framework overcomes the limitations of current ad hoc or supervised energy-based or Markovian models that often involve many parameters to adapt and that are finely tuned for each different benchmark database. Experimental results show that the proposed algorithm performs favorably against state-of-the-art methods and turns out to be particularly stable across a wide variety of benchmark datasets.

Untargeted metabolomics analysis based on LC-IM-QTOF-MS for discriminating geographical origin and vintage of Chinese red wine

Identifying wine geographical origin and vintage is vital due to the abundance of fraudulent activity associated with wine mislabeling of region and vintage. In this study, an untargeted metabolomic approach based on liquid chromatography/ion mobility quadrupole time-of-flight mass spectrometry (LC-IM-QTOF-MS) was used to discriminate wine geographical origin and vintage. Wines were well discriminated according to region and vintage with orthogonal partial least squares-discriminant analysis (OPLS-DA). The differential metabolites subsequently were screened by OPLS-DA with pairwise modeling. 42 and 48 compounds in positive and negative ionization modes were screened as differential metabolitesfor the discrimination of different wine regions, and 37 and 35 compounds were screened for wine vintage. Furthermore, new OPLS-DA models were performed using these compounds, and the external verification trial showed excellent practicality with an accuracy over 84.2%. This study indicated that LC-IM-QTOF-MS-based untargeted metabolomics was a feasible tool for wine geographical origin and vintage discrimination.

Extent of resection in patients with glioblastoma

To investigate the impact of resection quality on subsequent survival of patients with glioblastoma. There were 141 patients with morphologically confirmed glioblastoma (grade 4). Fractionation with the prescribed dose of 2 and 3 Gy was alternately used (pairwise modeling strategy). Total resection was performed in 29.8% of patients (EOR: 100%; n=42), subtotal - 56.7% (EOR: 70-99%; n=80). Extent of resection 1-69% was registered in 19 patients (13.5%). As of December 2022, 124 out of 141 patients (87.9%) were diagnosed with primary progression, 101 (71.6%) ones died. We analyzed the threshold role of EOR. The most informative level was 70% (p=0.002). EOR 100% was followed by median overall survival about 32.2 months (95% Cl: 15.3-49.1), EOR 70-99% - 21.3 months (95% Cl: 15.1-27.5), EOR 1-69% - 10.3 months (95% Cl: 3.8-16.9; p=0.003). Fractionation mode with the prescribed dose of 3 Gy partially eliminated significance of EOR (p=0.148) in contrast to standard fractionation (p=0.015). Tumor growth in the interval between surgery and radiotherapy (REP) reduces significance of EOR (p=0.042). Inclusion of second-line therapy with bevacizumab in multivariate analysis model (OR=0.488; p=0.002) makes EOR less significant (OR=0.749; p=0.085) in contrast to REP (OR=2.482; p<0.0001). To date, the principle of maximum safe resection remains fundamental in neurosurgery. EOR about 70% is sufficient regarding overall survival, but total resection should be sought if possible.

Untargeted metabolomic analysis of Chinese red wines for geographical origin traceability by UPLC-QTOF-MS coupled with chemometrics

Identifying geographical origins of red wines made in specific regions is of significance since the false claim of geographical origins has been frequently exposed in China's wine industry. In this work, an untargeted metabolomic approach based on UPLC-QTOF-MS was established to discriminate geographical origins of Chinese red wines. The principal component analysis (PCA) showed significant differences between wine samples from three famous geographical origins in China. The metabolites contributing to the differentiation were screened by orthogonal partial least squares-discriminant analysis (OPLS-DA) with pairwise modeling. 40 and 46 differential metabolites in positive and negative ionization modes were putatively identified as chemical markers. Furthermore, heatmap visualization and OPLS-DA models were constructed based on these identified markers and external verification wine samples from different regions were successfully discriminated, with recognition rate up to 96.7%. This study indicated that UPLC-QTOF-MS-based untargeted metabolomics has great potential for the geographical origin traceability of Chinese red wines.

Complete Genome Characterization of Reticuloendotheliosis Virus Detected in Chickens with Multiple Viral Coinfections.

Reticuloendotheliosis virus (REV) is a retroviral pathogen capable of infecting several avian hosts and is associated with immunosuppression, anemia, proventriculitis, neoplasia, and runting–stunting syndrome. Its genome contains the three major genes, gag, pol, and env, and two flanking long terminal repeat (LTR) regions. Complete genome sequences of REV are limited in terms of geographical origin. The aim of this study was to characterize the complete genome of REV detected in Brazilian chickens with multiple viral coinfections and analyze the polymorphisms in the deduced amino acids sequences corresponding to its encoded proteins. We tested the presence and completeness of REV as well as other viral pathogens in samples from Brazilian poultry farms by qPCR. The complete genomes of two REV strains were sequenced by overlapping fragments through the dideoxy method. Phylogenetic analysis, pairwise identity matrix, polymorphism identification and protein modeling were performed along the entire genome. We detected REV in 65% (26/40) of the tested samples. Concomitant viral infections were detected in 82.5% (33/40) of the samples and in 90% (9/10) of the farms. Multiple infections included up to seven viruses. Phylogenetic analysis classified both Brazilian strains into REV subtype 3, and the pairwise comparison indicated that strains from the USA and fowlpox virus (FWPV)-related strains were the most identical. The subdomain p18 in gag, the reverse transcriptase/ribonuclease H in pol, and the surface (SU) in the env protein were the most polymorphic in genomic comparisons. The relevant motifs for each protein were highly conserved, with fewer polymorphisms in the fusion peptide, immunosuppression domain, and disulfide bonds on the surface (SU) and transmembrane (TM) of env. This is the first study to include complete genomes of REV in Brazil and South America detected in farms with multiple viral coinfections. Our findings suggest an involvement of REV as an immunosuppressor and active agent in the emergence and progression of multiple infectious diseases. We also found a possible etiological relationship between Brazilian strains and the USA and FWPV recombinant strains. This information highlights the need for epidemiological vigilance regarding REV in association with another pathogens.

Pairwise joint modeling of clustered and high-dimensional outcomes with covariate missingness in pediatric pneumonia care.

Multiple outcomes reflecting different aspects of routine care are a common phenomenon in health care research. A common approach of handling such outcomes is multiple univariate analyses, an approach which does not allow for answering research questions pertaining to joint inference. In this study, we sought to study associations among nine pediatric pneumonia care outcomes spanning assessment, diagnosis and treatment domains of care, while circumventing the computational challenge posed by their clustered and high-dimensional nature and incompletely recorded covariates. We analyzed data from a cluster randomized trial conducted in 12 Kenyan hospitals. There were varying degrees of missingness in the covariates of interest, and these were multiply imputed using latent normal joint modeling. We used the pairwise joint modeling strategy to fit a correlated random effects joint model for the nine outcomes. This entailed fitting 36 bivariate generalized linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We also analyzed the nine outcomes separately before and after multiple imputation. We observed joint effects of patient-, clinician- and hospital-level factors on pneumonia care indicators before and after multiple imputation of missing covariates. In both pairwise joint modeling and separate univariate analysis methods, enhanced audit and feedback improved documentation and adherence to recommended clinical guidelines over time in six and five pneumonia care indicators, respectively. Additionally, multiple imputation improved precision of parameter estimates compared to complete case analysis. The strength and direction of association among pneumonia outcomes varied within and across the three domains of pneumonia care

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.

Gibberellins regulate lateral root development that is associated with auxin and cell wall metabolisms in cucumber

Cucumber is an economically important crop cultivated worldwide. Gibberellins (GAs) play important roles in the development of lateral roots (LRs), which are critical for plant stress tolerance and productivity. Therefore, it is of great importance for cucumber production to study the role of GAs in LR development. Here, the results showed that GAs regulated cucumber LR development in a concentration-dependent manner. Treatment with 1, 10, 50 and 100 μM GA3 significantly increased secondary root length, tertiary root number and length. Of these, 50 μM GA3 treatment had strong effects on increasing root dry weight and the root/shoot dry weight ratio. Pairwise comparisons identified 417 down-regulated genes enriched for GA metabolism-related processes and 447 up-regulated genes enriched for cell wall metabolism-related processes in GA3-treated roots. A total of 3523 non-redundant DEGs were identified in our RNA-Seq data through pairwise comparisons and linear factorial modeling. Of these, most of the genes involved in auxin and cell wall metabolisms were up-regulated in GA3-treated roots. Our findings not only shed light on LR regulation mediated by GA but also offer an important resource for functional studies of candidate genes putatively involved in the regulation of LR development in cucumber and other crops.

Beyond exposure-response: A tutorial on statistical considerations in dose-ranging studies.

Dose‐ranging studies are a crucial part of the phase II drug development process. They complement the understanding gained from exposure‐response analyses. However, the statistical design issues related to dose‐ranging studies are not always keenly understood and a poorly designed study can be costly for later development. In this tutorial, we review five key statistical principles in designing such a study. We also describe some popular statistical approaches, including pairwise comparison, modeling, and Multiple Comparison Procedure modeling in the context of principles.

Align R-CNN: A Pairwise Head Network for Visual Relationship Detection

Scene graphs connect individual objects with visual relationships. They serve as a comprehensive scene representation for downstream multimodal tasks. However, by exploring recent progress in Scene Graph Generation (SGG), we find that the performance of recent works is highly limited by the pairwise relationship modeling by naive feature concatenation. Such pairwise features lack sufficient object interaction due to the mis-aligned object parts, resulting in non-discriminative pairwise features for visual relationship prediction. For example, naive concatenated pairwise feature usually make the model fail to discriminate between <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">riding</monospace> and <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feeding</monospace> for object pair <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">person</monospace> and <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">horse</monospace> . To this end, we design a meta-architecture— learning-to-align — for dynamic object feature concatenation. We call our model: <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Align R-CNN</b> . Specifically, we introduce a novel attention-based multiple region alignment module that can be jointly optimized with SGG. Experiments on the large-scale SGG benchmark Visual Genome show that the proposed <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Align R-CNN</b> can replace the naive feature concatenation and thus boost all the existing SGG methods.

SAM: Modeling Scene, Object and Action With Semantics Attention Modules for Video Recognition

Video recognition aims at understanding semantic contents that normally involve the interactions of humans and related objects under certain scenes. A common practice to improve recognition accuracy is to combine object, scene and action features for classification directly, assuming that they are explicitly complementary. In this paper, we break down the fusion of three features into two pairwise feature relation modeling processes, which mitigates the difficulty of correlation learning in high dimensional features. Towards this goal, we introduce a Semantics Attention Module that captures the relations of a pair of features by refining the relatively “weak” feature with the guidance from the “strong” feature using attention mechanisms. The refined representation is further combined with the “strong” feature using a residual design for downstream tasks. Two SAMs are applied in a Semantics Attention Network (SAN) for improving video recognition. Extensive experiments are conducted on two large-scale video benchmarks, FCVID and ActivityNet v1.3—the proposed approach achieves better results while requiring much less computational effort than alternative methods.

Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach.

Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities amongst outputs employs a convolution process (CP). The CP is based on the idea of sharing latent functions across several convolutions. Despite the elegance of the CP construction, it provides new challenges that need yet to be tackled. First, even with a moderate number of outputs, model building is extremely prohibitive due to the huge increase in computational demands and number of parameters to be estimated. Second, the negative transfer of knowledge may occur when some outputs do not share commonalities. In this paper we address these issues. We propose a regularized pairwise modeling approach for the MGP established using CP. The key feature of our approach is to distribute the estimation of the full multivariate model into a group of bivariate GPs which are individually built. Interestingly pairwise modeling turns out to possess unique characteristics, which allows us to tackle the challenge of negative transfer through penalizing the latent function that facilitates information sharing in each bivariate model. Predictions are then made through combining predictions from the bivariate models within a Bayesian framework. The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs. Statistical guarantees for the proposed method are studied and its advantageous features are demonstrated through numerical studies.