High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of infinitesimal generator or transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.
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Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which directly discretize Langevin dynamics to estimate expectations over the target distribution. We study the use of transport maps that approximately normalize a target distribution as a way to precondition and accelerate the convergence of Langevin dynamics. We show that in continuous time, when a transport map is applied to Langevin dynamics, the result is a Riemannian manifold Langevin dynamics (RMLD) with metric defined by the transport map. We also show that applying a transport map to an irreversibly-perturbed ULA results in a geometry-informed irreversible perturbation (GiIrr) of the original dynamics. These connections suggest more systematic ways of learning metrics and perturbations, and also yield alternative discretizations of the RMLD described by the map, which we study. Under appropriate conditions, these discretized processes can be endowed with non-asymptotic bounds describing convergence to the target distribution in 2-Wasserstein distance. Illustrative numerical results complement our theoretical claims.
We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range, distance-dependent ``interactions'' without assuming a specific form for the underlying probability distribution. Predictions are obtained by means of a fully autonomous learning algorithm which employs equilibrium conditional Monte Carlo simulations. MPRS is able to handle scattered data and arbitrary spatial dimensions. We report tests on various synthetic and real-word data in one, two and three dimensions which demonstrate that the MPRS prediction performance (without parameter tuning) is competitive with standard interpolation methods such as ordinary kriging and inverse distance weighting. In particular, MPRS is a particularly effective gap-filling method for rough and non-Gaussian data (e.g., daily precipitation time series). MPRS shows superior computational efficiency and scalability for large samples. Massive data sets involving millions of nodes can be processed in a few seconds on a standard personal computer.
The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming. The complex cross-scale interactions of processes that produce precipitation are challenging to model, however, inducing potentially strong biases in ESM fields, especially regarding extremes. State-of-the-art bias correction methods only address errors in the simulated frequency distributions locally at every individual grid cell. Improving unrealistic spatial patterns of the ESM output, which would require spatial context, has not been possible so far. Here, we show that a post-processing method based on physically constrained generative adversarial networks (cGANs) can correct biases of a state-of-the-art, CMIP6-class ESM both in local frequency distributions and in the spatial patterns at once. While our method improves local frequency distributions equally well as gold-standard bias-adjustment frameworks, it strongly outperforms any existing methods in the correction of spatial patterns, especially in terms of the characteristic spatial intermittency of precipitation extremes.
Automatic analysis of colonoscopy images has been an active field of research motivated by the importance of early detection of precancerous polyps. However, detecting polyps during the live examination can be challenging due to various factors such as variation of skills and experience among the endoscopists, lack of attentiveness, and fatigue leading to a high polyp miss-rate. Deep learning has emerged as a promising solution to this challenge as it can assist endoscopists in detecting and classifying overlooked polyps and abnormalities in real time. In addition to the algorithm's accuracy, transparency and interpretability are crucial to explaining the whys and hows of the algorithm's prediction. Further, most algorithms are developed in private data, closed source, or proprietary software, and methods lack reproducibility. Therefore, to promote the development of efficient and transparent methods, we have organized the "Medico automatic polyp segmentation (Medico 2020)" and "MedAI: Transparency in Medical Image Segmentation (MedAI 2021)" competitions. We present a comprehensive summary and analyze each contribution, highlight the strength of the best-performing methods, and discuss the possibility of clinical translations of such methods into the clinic. For the transparency task, a multi-disciplinary team, including expert gastroenterologists, accessed each submission and evaluated the team based on open-source practices, failure case analysis, ablation studies, usability and understandability of evaluations to gain a deeper understanding of the models' credibility for clinical deployment. Through the comprehensive analysis of the challenge, we not only highlight the advancements in polyp and surgical instrument segmentation but also encourage qualitative evaluation for building more transparent and understandable AI-based colonoscopy systems.
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric families of mechanistic models (MM). Two classes of methodologies, based on Bayesian inference and Population of Models, currently prevail in parameter estimation for physical systems. However, in Bayesian analysis, uninformative priors for MM parameters introduce undesirable bias. Here, we propose how to infer parameters within the framework of stochastic inverse problems (SIP), also termed data-consistent inversion, wherein the prior targets only uncertainties that arise due to MM non-invertibility. To demonstrate, we introduce new methods to solve SIP based on rejection sampling, Markov chain Monte Carlo, and generative adversarial networks (GANs). In addition, to overcome limitations of SIP, we reformulate SIP based on constrained optimization and present a novel GAN to solve the constrained optimization problem.
Reinforcement learning(RL) algorithms face the challenge of limited data efficiency, particularly when dealing with high-dimensional state spaces and large-scale problems. Most of RL methods often rely solely on state transition information within the same episode when updating the agent's Critic, which can lead to low data efficiency and sub-optimal training time consumption. Inspired by human-like analogical reasoning abilities, we introduce a novel mesh information propagation mechanism, termed the 'Imagination Mechanism (IM)', designed to significantly enhance the data efficiency of RL algorithms. Specifically, IM enables information generated by a single sample to be effectively broadcasted to different states across episodes, instead of simply transmitting in the same episode. This capability enhances the model's comprehension of state interdependencies and facilitates more efficient learning of limited sample information. To promote versatility, we extend the IM to function as a plug-and-play module that can be seamlessly and fluidly integrated into other widely adopted RL algorithms. Our experiments demonstrate that IM consistently boosts four mainstream SOTA RL algorithms, such as SAC, PPO, DDPG, and DQN, by a considerable margin, ultimately leading to superior performance than before across various tasks. For access to our code and data, please visit //github.com/OuAzusaKou/imagination_mechanism
The aim of this study is to analyze the effect of serum metabolites on diabetic nephropathy (DN) and predict the prevalence of DN through a machine learning approach. The dataset consists of 548 patients from April 2018 to April 2019 in Second Affiliated Hospital of Dalian Medical University (SAHDMU). We select the optimal 38 features through a Least absolute shrinkage and selection operator (LASSO) regression model and a 10-fold cross-validation. We compare four machine learning algorithms, including eXtreme Gradient Boosting (XGB), random forest, decision tree and logistic regression, by AUC-ROC curves, decision curves, calibration curves. We quantify feature importance and interaction effects in the optimal predictive model by Shapley Additive exPlanations (SHAP) method. The XGB model has the best performance to screen for DN with the highest AUC value of 0.966. The XGB model also gains more clinical net benefits than others and the fitting degree is better. In addition, there are significant interactions between serum metabolites and duration of diabetes. We develop a predictive model by XGB algorithm to screen for DN. C2, C5DC, Tyr, Ser, Met, C24, C4DC, and Cys have great contribution in the model, and can possibly be biomarkers for DN.
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors with independent coordinates having ordinary smooth densities, we derive an inversion inequality relating the $L^1$-Wasserstein distance between two distributions of the signal to the $L^1$-distance between the corresponding mixture densities of the observations. This smoothing inequality outperforms existing inversion inequalities. As an application of the inversion inequality to the Bayesian framework, we consider $1$-Wasserstein deconvolution with Laplace noise in dimension one using a Dirichlet process mixture of normal densities as a prior measure on the mixing distribution (or distribution of the signal). We construct an adaptive approximation of the sampling density by convolving the Laplace density with a well-chosen mixture of normal densities and show that the posterior measure concentrates around the sampling density at a nearly minimax rate, up to a log-factor, in the $L^1$-distance. The same posterior law is also shown to automatically adapt to the unknown Sobolev regularity of the mixing density, thus leading to a new Bayesian adaptive estimation procedure for mixing distributions with regular densities under the $L^1$-Wasserstein metric. We illustrate utility of the inversion inequality also in a frequentist setting by showing that an appropriate isotone approximation of the classical kernel deconvolution estimator attains the minimax rate of convergence for $1$-Wasserstein deconvolution in any dimension $d\geq 1$, when only a tail condition is required on the latent mixing density and we derive sharp lower bounds for these problems
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.
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