The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.
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Generative diffusion models have achieved spectacular performance in many areas of generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We argue that this lead to a form of instability that lies at the heart of their generative capabilities and that can be described by a set of mean field critical exponents. We conclude by analyzing recent work connecting diffusion models and associative memory networks in view of the thermodynamic formulations.
Bayesian optimal design of experiments is a well-established approach to planning experiments. Briefly, a probability distribution, known as a statistical model, for the responses is assumed which is dependent on a vector of unknown parameters. A utility function is then specified which gives the gain in information for estimating the true value of the parameters using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising the expectation of the utility with respect to the joint distribution given by the statistical model and prior distribution for the true parameter values. The approach takes account of the experimental aim via specification of the utility and of all assumed sources of uncertainty via the expected utility. However, it is predicated on the specification of the statistical model. Recently, a new type of statistical inference, known as Gibbs (or General Bayesian) inference, has been advanced. This is Bayesian-like, in that uncertainty on unknown quantities is represented by a posterior distribution, but does not necessarily rely on specification of a statistical model. Thus the resulting inference should be less sensitive to misspecification of the statistical model. The purpose of this paper is to propose Gibbs optimal design: a framework for optimal design of experiments for Gibbs inference. The concept behind the framework is introduced along with a computational approach to find Gibbs optimal designs in practice. The framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.
Statistical models should accurately reflect analysts' domain knowledge about variables and their relationships. While recent tools let analysts express these assumptions and use them to produce a resulting statistical model, it remains unclear what analysts want to express and how externalization impacts statistical model quality. This paper addresses these gaps. We first conduct an exploratory study of analysts using a domain-specific language (DSL) to express conceptual models. We observe a preference for detailing how variables relate and a desire to allow, and then later resolve, ambiguity in their conceptual models. We leverage these findings to develop rTisane, a DSL for expressing conceptual models augmented with an interactive disambiguation process. In a controlled evaluation, we find that rTisane's DSL helps analysts engage more deeply with and accurately externalize their assumptions. rTisane also leads to statistical models that match analysts' assumptions, maintain analysis intent, and better fit the data.
We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the probabilistic stability regions and benchmark them against the absolute stability regions for deterministic Taylor schemes.
Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional asymptotics regime, in which the ratio of the number of features to the number of observations converges to a constant. Specifically, we propose a general strategy to analyze the prediction risk under squared error loss of bagged predictors using classical results on simple random sampling. Specializing the strategy, we derive the exact asymptotic risk of the bagged ridge and ridgeless predictors with an arbitrary number of bags under a well-specified linear model with arbitrary feature covariance matrices and signal vectors. Furthermore, we prescribe a generic cross-validation procedure to select the optimal subsample size for bagging and discuss its utility to eliminate the non-monotonic behavior of the limiting risk in the sample size (i.e., double or multiple descents). In demonstrating the proposed procedure for bagged ridge and ridgeless predictors, we thoroughly investigate the oracle properties of the optimal subsample size and provide an in-depth comparison between different bagging variants.
Supervised deep learning was recently introduced in high-contrast imaging (HCI) through the SODINN algorithm, a convolutional neural network designed for exoplanet detection in angular differential imaging (ADI) datasets. The benchmarking of HCI algorithms within the Exoplanet Imaging Data Challenge (EIDC) showed that (i) SODINN can produce a high number of false positives in the final detection maps, and (ii) algorithms processing images in a more local manner perform better. This work aims to improve the SODINN detection performance by introducing new local processing approaches and adapting its learning process accordingly. We propose NA-SODINN, a new deep learning binary classifier based on a convolutional neural network (CNN) that better captures image noise correlations in ADI-processed frames by identifying noise regimes. Our new approach was tested against its predecessor, as well as two SODINN-based hybrid models and a more standard annular-PCA approach, through local receiving operating characteristics (ROC) analysis of ADI sequences from the VLT/SPHERE and Keck/NIRC-2 instruments. Results show that NA-SODINN enhances SODINN in both sensitivity and specificity, especially in the speckle-dominated noise regime. NA-SODINN is also benchmarked against the complete set of submitted detection algorithms in EIDC, in which we show that its final detection score matches or outperforms the most powerful detection algorithms.Throughout the supervised machine learning case, this study illustrates and reinforces the importance of adapting the task of detection to the local content of processed images.
Semi-supervised learning (SSL) has become popular in recent years because it allows the training of a model using a large amount of unlabeled data. However, one issue that many SSL methods face is the confirmation bias, which occurs when the model is overfitted to the small labeled training dataset and produces overconfident, incorrect predictions. To address this issue, we propose SequenceMatch, an efficient SSL method that utilizes multiple data augmentations. The key element of SequenceMatch is the inclusion of a medium augmentation for unlabeled data. By taking advantage of different augmentations and the consistency constraints between each pair of augmented examples, SequenceMatch helps reduce the divergence between the prediction distribution of the model for weakly and strongly augmented examples. In addition, SequenceMatch defines two different consistency constraints for high and low-confidence predictions. As a result, SequenceMatch is more data-efficient than ReMixMatch, and more time-efficient than both ReMixMatch ($\times4$) and CoMatch ($\times2$) while having higher accuracy. Despite its simplicity, SequenceMatch consistently outperforms prior methods on standard benchmarks, such as CIFAR-10/100, SVHN, and STL-10. It also surpasses prior state-of-the-art methods by a large margin on large-scale datasets such as ImageNet, with a 38.46\% error rate. Code is available at //github.com/beandkay/SequenceMatch.
Meta-analysis is the aggregation of data from multiple studies to find patterns across a broad range relating to a particular subject. It is becoming increasingly useful to apply meta-analysis to summarize these studies being done across various fields. In meta-analysis, it is common to use the mean and standard deviation from each study to compare for analysis. While many studies reported mean and standard deviation for their summary statistics, some report other values including the minimum, maximum, median, and first and third quantiles. Often, the quantiles and median are reported when the data is skewed and does not follow a normal distribution. In order to correctly summarize the data and draw conclusions from multiple studies, it is necessary to estimate the mean and standard deviation from each study, considering variation and skewness within each study. In past literature, methods have been proposed to estimate the mean and standard deviation, but do not consider negative values. Data that include negative values are common and would increase the accuracy and impact of the me-ta-analysis. We propose a method that implements a generalized Box-Cox transformation to estimate the mean and standard deviation accounting for such negative values while maintaining similar accuracy.
The generative adversarial network (GAN) is an important model developed for high-dimensional distribution learning in recent years. However, there is a pressing need for a comprehensive method to understand its error convergence rate. In this research, we focus on studying the error convergence rate of the GAN model that is based on a class of functions encompassing the discriminator and generator neural networks. These functions are VC type with bounded envelope function under our assumptions, enabling the application of the Talagrand inequality. By employing the Talagrand inequality and Borel-Cantelli lemma, we establish a tight convergence rate for the error of GAN. This method can also be applied on existing error estimations of GAN and yields improved convergence rates. In particular, the error defined with the neural network distance is a special case error in our definition.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
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