Continual Invariant Risk Minimization

Empirical risk minimization can lead to poor generalization behavior on unseen environments if the learned model does not capture invariant feature representations. Invariant risk minimization (IRM) is a recent proposal for discovering environment-invariant representations. IRM was introduced by Arjovsky et al. (2019) and extended by Ahuja et al. (2020). IRM assumes that all environments are available to the learning system at the same time. With this work, we generalize the concept of IRM to scenarios where environments are observed sequentially. We show that existing approaches, including those designed for continual learning, fail to identify the invariant features and models across sequentially presented environments. We extend IRM under a variational Bayesian and bilevel framework, creating a general approach to continual invariant risk minimization. We also describe a strategy to solve the optimization problems using a variant of the alternating direction method of multiplier (ADMM). We show empirically using multiple datasets and with multiple sequential environments that the proposed methods outperform or is competitive with prior approaches.Comment: Shorter version of this paper was presented at RobustML workshop of ICLR 202

Self-Tuning Hamiltonian Monte Carlo for Accelerated Sampling

The performance of Hamiltonian Monte Carlo crucially depends on its parameters, in particular the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune these parameters based on a loss function which promotes the fast exploration of phase-space. For this, we make use of a fully-differentiable set-up and use backpropagation for optimization. An attention-like loss is defined which allows for the gradient driven learning of the distribution of integration steps. We also highlight the importance of jittering for a smooth loss-surface. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test-case for simulation methods. We find a good correspondence between our loss and the autocorrelation times, resulting in well-tuned parameters for Hamiltonian Monte Carlo

Learning Neural PDE Solvers with Parameter-Guided Channel Attention

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.Comment: accepted for publication in ICML202

Efficient and Scalable Multi-task Regression on Massive Number of Tasks

Many real-world large-scale regression problems can be formulated as Multi-task Learning (MTL) problems with a massive number of tasks, as in retail and transportation domains. However, existing MTL methods still fail to offer both the generalization performance and the scalability for such problems. Scaling up MTL methods to problems with a tremendous number of tasks is a big challenge. Here, we propose a novel algorithm, named Convex Clustering Multi-Task regression Learning (CCMTL), which integrates with convex clustering on the k-nearest neighbor graph of the prediction models. Further, CCMTL efficiently solves the underlying convex problem with a newly proposed optimization method. CCMTL is accurate, efficient to train, and empirically scales linearly in the number of tasks. On both synthetic and real-world datasets, the proposed CCMTL outperforms seven state-of-the-art (SoA) multi-task learning methods in terms of prediction accuracy as well as computational efficiency. On a real-world retail dataset with 23,812 tasks, CCMTL requires only around 30 seconds to train on a single thread, while the SoA methods need up to hours or even days.Comment: Accepted at AAAI 201

Measuring the Discrepancy between Conditional Distributions: Methods, Properties and Applications

We propose a simple yet powerful test statistic to quantify the discrepancy between two conditional distributions. The new statistic avoids the explicit estimation of the underlying distributions in highdimensional space and it operates on the cone of symmetric positive semidefinite (SPS) matrix using the Bregman matrix divergence. Moreover, it inherits the merits of the correntropy function to explicitly incorporate high-order statistics in the data. We present the properties of our new statistic and illustrate its connections to prior art. We finally show the applications of our new statistic on three different machine learning problems, namely the multi-task learning over graphs, the concept drift detection, and the information-theoretic feature selection, to demonstrate its utility and advantage. Code of our statistic is available at https://bit.ly/BregmanCorrentropy.Comment: manuscript accepted at IJCAI 20; added additional notes on computational complexity and auto-differentiable property; code is available at https://github.com/SJYuCNEL/Bregman-Correntropy-Conditional-Divergenc

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBench, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBench comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBench allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.Comment: 16 pages (main body) + 34 pages (supplemental material), accepted for publication in NeurIPS 2022 Track Datasets and Benchmark

SNPs Array Karyotyping Reveals a Novel Recurrent 20p13 Amplification in Primary Myelofibrosis

The molecular pathogenesis of primary mielofibrosis (PMF) is still largely unknown. Recently, single-nucleotide polymorphism arrays (SNP-A) allowed for genome-wide profiling of copy-number alterations and acquired uniparental disomy (aUPD) at high-resolution. In this study we analyzed 20 PMF patients using the Genome-Wide Human SNP Array 6.0 in order to identify novel recurrent genomic abnormalities. We observed a complex karyotype in all cases, detecting all the previously reported lesions (del(5q), del(20q), del(13q), +8, aUPD at 9p24 and abnormalities on chromosome 1). In addition, we identified several novel cryptic lesions. In particular, we found a recurrent alteration involving cytoband 20p13 in 55% of patients. We defined a minimal affected region (MAR), an amplification of 9,911 base-pair (bp) overlapping the SIRPB1 gene locus. Noteworthy, by extending the analysis to the adjacent areas, the cytoband was overall affected in 95% of cases. Remarkably, these results were confirmed by real-time PCR and validated in silico in a large independent series of myeloproliferative diseases. Finally, by immunohistochemistry we found that SIRPB1 was over-expressed in the bone marrow of PMF patients carrying 20p13 amplification. In conclusion, we identified a novel highly recurrent genomic lesion in PMF patients, which definitely warrant further functional and clinical characterization