Fluid dynamics modeling has received extensive attention in the machine learning community. Although numerous graph neural network (GNN) approaches have been proposed for this problem, the problem of out-of-distribution (OOD) generalization remains underexplored. In this work, we propose a new large-scale dataset Prometheus which simulates tunnel and pool fires across various environmental conditions and builds an extensive benchmark of 12 baselines, which demonstrates that the OOD generalization performance is far from satisfactory. To tackle this, this paper introduces a new approach named Disentangled Graph ODE (DGODE), which learns disentangled representations for continuous interacting dynamics modeling. In particular, we utilize a temporal GNN and a frequency network to extract semantics from historical trajectories into node representations and environment representations respectively. To mitigate the potential distribution shift, we minimize the mutual information between invariant node representations and the discretized environment features using adversarial learning. Then, they are fed into a coupled graph ODE framework, which models the evolution using neighboring nodes and dynamical environmental context. In addition, we enhance the stability of the framework by perturbing the environment features to enhance robustness. Extensive experiments validate the effectiveness of DGODE compared with state-of-the-art approaches.

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate for the oracle estimator obtained as if all data were available simultaneously. Next, we consider a family of generalized $\ell_2$-regularization algorithms indexed by matrix-valued hyperparameters, which includes the minimum norm estimator and continual ridge regression as special cases. As more tasks are introduced, we derive an iterative update formula for the estimation error of generalized $\ell_2$-regularized estimators, from which we determine the hyperparameters resulting in the optimal algorithm. Interestingly, the choice of hyperparameters can effectively balance the trade-off between forward and backward knowledge transfer and adjust for data heterogeneity. Moreover, the estimation error of the optimal algorithm is derived explicitly, which is of the same order as that of the oracle estimator. In contrast, our lower bounds for the minimum norm estimator and continual ridge regression show their suboptimality. A byproduct of our theoretical analysis is the equivalence between early stopping and generalized $\ell_2$-regularization in continual learning, which may be of independent interest. Finally, we conduct experiments to complement our theory.

Conventional wisdom in machine learning holds that the more data you train your model on, the better the model can perform. Accordingly, a plethora of federated learning methods have been developed to aggregate as many local samples as possible. Contrary to this belief, this paper shows that aggregation of more data is not necessarily beneficial in the presence of heterogeneity, and reveals a fundamental trade-off between aggregation and heterogeneity in federated learning. We consider a general family of weighted $M$-estimators that interpolate between FedAvg and the local estimator, in which an aggregation rule is determined by the weights of local samples. We derive an upper bound for the estimation error of the weighted $M$-estimators, which decomposes into a bias term induced by heterogeneity and a variance term influenced by aggregation. A measure of heterogeneity, the federated smoothness $\beta$, is introduced to simplify the general result. As an important consequence, the optimal aggregation rule for each local device is to aggregate only its $\lfloor K^{2\beta/(2\beta+1)}/(n/\sigma^2)^{1/(2\beta+1)}\rfloor\vee 1$ closest neighbors among the $K$ devices, where $n$ is the local sample size and $\sigma^2$ is the noise variance. Moreover, we show that our estimator, termed FedKNN, attains the minimax optimal rate over a certain parameter space characterized by $\beta$. This optimal procedure depends crucially on the neighboring structure among devices in terms of the proximity of local parameters. Finally, we prove that without such prior knowledge no estimator can achieve a convergence rate faster than $O(\sigma^2/n)$ and hence adaptation is impossible.

This study considers the estimation of conditional causal effects in the presence of unmeasured confounding for a balanced panel with treatment imposed at the last time point. To address this, we combine Difference-in-differences (DiD) and tree-based methods and propose a new identification assumption that allows for the violation of the (conditional) parallel trends assumption adopted by most existing DiD methods. Under this new assumption, we prove partial identifiability of the conditional average treatment effect on the treated group (CATT). Our proposed method estimates CATT through a tree-based causal approach, guided by a novel splitting rule that avoids model misspecification and unnecessary auxiliary parameter estimation. The splitting rule measures both the error of fitting observed data and the violation of conditional parallel trends simultaneously. We also develop an ensemble of multiple trees via gradient boosting to further enhance performance. Experimental results on both synthetic and real-world datasets validate the effectiveness of our proposed method.

Unmeasured confounding poses a significant threat to the validity of causal inference. Despite that various ad hoc methods are developed to remove confounding effects, they are subject to certain fairly strong assumptions. In this work, we consider the estimation of conditional causal effects in the presence of unmeasured confounding using observational data and historical controls. Under an interpretable transportability condition, we prove the partial identifiability of conditional average treatment effect on the treated group (CATT). For tree-based models, a new notion, \emph{confounding entropy}, is proposed to measure the discrepancy introduced by unobserved confounders between the conditional outcome distribution of the treated and control groups. The confounding entropy generalizes conventional confounding bias, and can be estimated effectively using historical controls. We develop a new method, debiased causal tree, whose splitting rule is to minimize the empirical risk regularized by the confounding entropy. Notably, our method integrates current observational data (for empirical risk) and their historical controls (for confounding entropy) harmoniously. We highlight that, debiased causal tree can not only estimate CATT well in the presence of unmeasured confounding, but also is a robust estimator of conditional average treatment effect (CATE) against the imbalance of the treated and control populations when all confounders are observed. An extension of combining multiple debiased causal trees to further reduce biases by gradient boosting is considered. The computational feasibility and statistical power of our method are evidenced by simulations and a study of a credit card balance dataset.

MOTIVATION: MicroRNA (miRNA) and alternative splicing (AS)-mediated post-transcriptional regulation has been extensively studied in most eukaryotes. However, the interplay between AS and miRNAs has not been explored in plants. To our knowledge, the overall profile of miRNA target sites in circular RNAs (circRNA) generated by alternative back splicing has never been reported previously. To address the challenge, we identified miRNA target sites located in alternatively spliced regions of the linear and circular splice isoforms using the up-to-date single-molecule real-time (SMRT) isoform sequencing (Iso-Seq) and Illumina sequencing data in eleven plant species. RESULTS: In total, we identified 399 401 and 114 574 AS events from linear and circular RNAs, respectively. Among them, there were 64 781 and 41 146 miRNA target sites located in linear and circular AS region, respectively. In addition, we found 38 913 circRNAs to be overlapping with 45 648 AS events of its own parent isoforms, suggesting circRNA regulation of AS of linear RNAs by forming R-loop with the genomic locus. Here, we present a comprehensive database of miRNA targets in alternatively spliced linear and circRNAs (ASmiR) and a web server for deposition and identification of miRNA target sites located in the alternatively spliced region of linear and circular RNAs. This database is accompanied by an easy-to-use web query interface for meaningful downstream analysis. Plant research community can submit user-defined datasets to the web service to search AS regions harboring small RNA target sites. In conclusion, this study provides an unprecedented resource to understand regulatory relationships between miRNAs and AS in both gymnosperms and angiosperms. AVAILABILITY AND IMPLEMENTATION: The readily accessible database and web-based tools are available at http://forestry.fafu.edu.cn/bioinfor/db/ASmiR. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Summary: The single-molecule real-time (SMRT) isoform sequencing (Iso-Seq) based on Pacific Bioscience (PacBio) platform has received increasing attention for its ability to explore full-length isoforms. Thus, comprehensive tools for Iso-Seq bioinformatics analysis are extremely useful. Here, we present a one-stop solution for Iso-Seq analysis, called PRAPI to analyze alternative transcription initiation (ATI), alternative splicing (AS), alternative cleavage and polyadenylation (APA), natural antisense transcripts (NAT), and circular RNAs (circRNAs) comprehensively. PRAPI is capable of combining Iso-Seq full-length isoforms with short read data, such as RNA-Seq or polyadenylation site sequencing (PAS-seq) for differential expression analysis of NAT, AS, APA and circRNAs. Furthermore, PRAPI can annotate new genes and correct mis-annotated genes when gene annotation is available. Finally, PRAPI generates high-quality vector graphics to visualize and highlight the Iso-Seq results. Availability and implementation: The Dockerfile of PRAPI is available at http://www.bioinfor.org/tool/PRAPI. Contact: [email protected].

A new feature extraction method for face recognition based on principal component analysis (PCA) and fractional-step linear discriminant analysis (F-LDA) is given in this paper. In order to reduce the computation complexity, PCA is first used to reduce the dimension. In addition, before using F-LDA, we transform the pooled within-class scatter matrix into an identity matrix. The proposed method is tested on AR and UMIST face databases. Experiment results show that our method gains higher classification accuracy than other existing methods used in the experiment.