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We propose a novel end-to-end neural network architecture that, once trained, directly outputs a probabilistic clustering of a batch of input examples in one pass. It estimates a distribution over the number of clusters k, and for each 1≤k≤kmax, a distribution over the individual cluster assignment for each data point. The network is trained in advance in a supervised fashion on separate data to learn grouping by any perceptual similarity criterion based on pairwise labels (same/different group). It can then be applied to different data containing different groups. We demonstrate promising performance on high-dimensional data like images (COIL-100) and speech (TIMIT). We call this “learning to cluster” and show its conceptual difference to deep metric learning, semi-supervise clustering and other related approaches while having the advantage of performing learnable clustering fully end-to-end.
Nowadays, the inexpensive memory space promotes an accelerating growth of stored image data. To exploit the data using supervised Machine or Deep Learning, it needs to be labeled. Manually labeling the vast amount of data is time-consuming and expensive, especially if human experts with specific domain knowledge are indispensable. Active learning addresses this shortcoming by querying the user the labels of the most informative images first. One way to obtain the ‘informativeness’ is by using uncertainty sampling as a query strategy, where the system queries those images it is most uncertain about how to classify. In this paper, we present a web-based active learning framework that helps to accelerate the labeling process. After manually labeling some images, the user gets recommendations of further candidates that could potentially be labeled equally (bulk image folder shift). We aim to explore the most efficient ‘uncertainty’ measure to improve the quality of the recommendations such that all images are sorted with a minimum number of user interactions (clicks). We conducted experiments using a manually labeled reference dataset to evaluate different combinations of classifiers and uncertainty measures. The results clearly show the effectiveness of an uncertainty sampling with bulk image shift recommendations (our novel method), which can reduce the number of required clicks to only around 20% compared to manual labeling.
This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical system (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and typically require calibration through error-correcting functions. The parameters of these error-correcting functions are determined during a calibration process. However, due to various sources of noise, these parameters cannot be determined with precision, making it desirable to incorporate uncertainty in the calibration models. Bayesian modeling offers a natural and complete way of reflecting uncertainty by treating the model parameters as variables rather than fixed values. In addition, Bayesian modeling enables the incorporation of prior knowledge, making it an ideal choice for calibration. Nevertheless, it is infrequently used in sensor calibration. This study introduces Bayesian methods for the calibration of MEMS accelerometer data in a straightforward manner using recent advances in probabilistic programming.
Deep neural networks have become a veritable alternative to classic speaker recognition and clustering methods in recent years. However, while the speech signal clearly is a time series, and despite the body of literature on the benefits of prosodic (suprasegmental) features, identifying voices has usually not been approached with sequence learning methods. Only recently has a recurrent neural network (RNN) been successfully applied to this task, while the use of convolutional neural networks (CNNs) (that are not able to capture arbitrary time dependencies, unlike RNNs) still prevails. In this paper, we show the effectiveness of RNNs for speaker recognition by improving state of the art speaker clustering performance and robustness on the classic TIMIT benchmark. We provide arguments why RNNs are superior by experimentally showing a “sweet spot” of the segment length for successfully capturing prosodic information that has been theoretically predicted in previous work.
Study design:
Retrospective, mono-centric cohort research study.
Objectives:
The purpose of this study is to validate a novel artificial intelligence (AI)-based algorithm against human-generated ground truth for radiographic parameters of adolescent idiopathic scoliosis (AIS).
Methods:
An AI-algorithm was developed that is capable of detecting anatomical structures of interest (clavicles, cervical, thoracic, lumbar spine and sacrum) and calculate essential radiographic parameters in AP spine X-rays fully automatically. The evaluated parameters included T1-tilt, clavicle angle (CA), coronal balance (CB), lumbar modifier, and Cobb angles in the proximal thoracic (C-PT), thoracic, and thoracolumbar regions. Measurements from 2 experienced physicians on 100 preoperative AP full spine X-rays of AIS patients were used as ground truth and to evaluate inter-rater and intra-rater reliability. The agreement between human raters and AI was compared by means of single measure Intra-class Correlation Coefficients (ICC; absolute agreement; .75 rated as excellent), mean error and additional statistical metrics.
Results:
The comparison between human raters resulted in excellent ICC values for intra- (range: .97-1) and inter-rater (.85-.99) reliability. The algorithm was able to determine all parameters in 100% of images with excellent ICC values (.78-.98). Consistently with the human raters, ICC values were typically smallest for C-PT (eg, rater 1A vs AI: .78, mean error: 4.7°) and largest for CB (.96, -.5 mm) as well as CA (.98, .2°).
Conclusions:
The AI-algorithm shows excellent reliability and agreement with human raters for coronal parameters in preoperative full spine images. The reliability and speed offered by the AI-algorithm could contribute to the efficient analysis of large datasets (eg, registry studies) and measurements in clinical practice.
Black-box variational inference (BBVI) is a technique to approximate the posterior of Bayesian models by optimization. Similar to MCMC, the user only needs to specify the model; then, the inference procedure is done automatically. In contrast to MCMC, BBVI scales to many observations, is faster for some applications, and can take advantage of highly optimized deep learning frameworks since it can be formulated as a minimization task. In the case of complex posteriors, however, other state-of-the-art BBVI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art BBVI methods, including normalizing flow-based BBVI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI compares favorably against other BBVI methods. Further, using BF-VI, we develop a Bayesian model for the semi-structured melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate, for the first time, the use of BBVI in semi-structured models.
Know when you don't know
(2018)
Deep convolutional neural networks show outstanding performance in image-based phenotype classification given that all existing phenotypes are presented during the training of the network. However, in real-world high-content screening (HCS) experiments, it is often impossible to know all phenotypes in advance. Moreover, novel phenotype discovery itself can be an HCS outcome of interest. This aspect of HCS is not yet covered by classical deep learning approaches. When presenting an image with a novel phenotype to a trained network, it fails to indicate a novelty discovery but assigns the image to a wrong phenotype. To tackle this problem and address the need for novelty detection, we use a recently developed Bayesian approach for deep neural networks called Monte Carlo (MC) dropout to define different uncertainty measures for each phenotype prediction. With real HCS data, we show that these uncertainty measures allow us to identify novel or unclear phenotypes. In addition, we also found that the MC dropout method results in a significant improvement of classification accuracy. The proposed procedure used in our HCS case study can be easily transferred to any existing network architecture and will be beneficial in terms of accuracy and novelty detection.
Probabilistic Short-Term Low-Voltage Load Forecasting using Bernstein-Polynomial Normalizing Flows
(2021)
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level. However, high fluctuations and increasing electrification cause huge forecast errors with traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus enables various applications in low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein-Polynomial Normalizing Flows where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities and also outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.
At present, the majority of the proposed Deep Learning (DL) methods provide point predictions without quantifying the model's uncertainty. However, a quantification of the reliability of automated image analysis is essential, in particular in medicine when physicians rely on the results for making critical treatment decisions. In this work, we provide an entire framework to diagnose ischemic stroke patients incorporating Bayesian uncertainty into the analysis procedure. We present a Bayesian Convolutional Neural Network (CNN) yielding a probability for a stroke lesion on 2D Magnetic Resonance (MR) images with corresponding uncertainty information about the reliability of the prediction. For patient-level diagnoses, different aggregation methods are proposed and evaluated, which combine the individual image-level predictions. Those methods take advantage of the uncertainty in the image predictions and report model uncertainty at the patient-level. In a cohort of 511 patients, our Bayesian CNN achieved an accuracy of 95.33% at the image-level representing a significant improvement of 2% over a non-Bayesian counterpart. The best patient aggregation method yielded 95.89% of accuracy. Integrating uncertainty information about image predictions in aggregation models resulted in higher uncertainty measures to false patient classifications, which enabled to filter critical patient diagnoses that are supposed to be closer examined by a medical doctor. We therefore recommend using Bayesian approaches not only for improved image-level prediction and uncertainty estimation but also for the detection of uncertain aggregations at the patient-level.
Rheumatoid arthritis is an autoimmune disease that causes chronic inflammation of synovial joints, often resulting in irreversible structural damage. The activity of the disease is evaluated by clinical examinations, laboratory tests, and patient self-assessment. The long-term course of the disease is assessed with radiographs of hands and feet. The evaluation of the X-ray images performed by trained medical staff requires several minutes per patient. We demonstrate that deep convolutional neural networks can be leveraged for a fully automated, fast, and reproducible scoring of X-ray images of patients with rheumatoid arthritis. A comparison of the predictions of different human experts and our deep learning system shows that there is no significant difference in the performance of human experts and our deep learning model.
Probabilistic Deep Learning
(2020)
Probabilistic Deep Learning is a hands-on guide to the principles that support neural networks. Learn to improve network performance with the right distribution for different data types, and discover Bayesian variants that can state their own uncertainty to increase accuracy. This book provides easy-to-apply code and uses popular frameworks to keep you focused on practical applications.
Contemporary empirical applications frequently require flexible regression models for complex response types and large tabular or non-tabular, including image or text, data. Classical regression models either break down under the computational load of processing such data or require additional manual feature extraction to make these problems tractable. Here, we present deeptrafo, a package for fitting flexible regression models for conditional distributions using a tensorflow backend with numerous additional processors, such as neural networks, penalties, and smoothing splines. Package deeptrafo implements deep conditional transformation models (DCTMs) for binary, ordinal, count, survival, continuous, and time series responses, potentially with uninformative censoring. Unlike other available methods, DCTMs do not assume a parametric family of distributions for the response. Further, the data analyst may trade off interpretability and flexibility by supplying custom neural network architectures and smoothers for each term in an intuitive formula interface. We demonstrate how to set up, fit, and work with DCTMs for several response types. We further showcase how to construct ensembles of these models, evaluate models using inbuilt cross-validation, and use other convenience functions for DCTMs in several applications. Lastly, we discuss DCTMs in light of other approaches to regression with non-tabular data.
The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural networks, variational inference is widely used to approximate difficult-to-compute posteriors by variational distributions. Usually, Gaussians are used as variational distributions (Gaussian-VI) which limits the quality of the approximation due to their limited flexibility. Transformation models on the other hand are flexible enough to fit any distribution. Here we present transformation model-based variational inference (TM-VI) and demonstrate that it allows to accurately approximate complex posteriors in models with one parameter and also works in a mean-field fashion for multi-parameter models like neural networks.
Deep neural networks (DNNs) are known for their high prediction performance, especially in perceptual tasks such as object recognition or autonomous driving. Still, DNNs are prone to yield unreliable predictions when encountering completely new situations without indicating their uncertainty. Bayesian variants of DNNs (BDNNs), such as MC dropout BDNNs, do provide uncertainty measures. However, BDNNs are slow during test time because they rely on a sampling approach. Here we present a single shot MC dropout approximation that preserves the advantages of BDNNs without being slower than a DNN. Our approach is to analytically approximate for each layer in a fully connected network the expected value and the variance of the MC dropout signal. We evaluate our approach on different benchmark datasets and a simulated toy example. We demonstrate that our single shot MC dropout approximation resembles the point estimate and the uncertainty estimate of the predictive distribution that is achieved with an MC approach, while being fast enough for real-time deployments of BDNNs.
Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows
(2023)
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level to increase efficiency and ensure reliable control. However, high fluctuations and increasing electrification cause huge forecast variability, not reflected in traditional point estimates. Probabilistic load forecasts take uncertainties into account and thus allow more informed decision-making for the planning and operation of low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein polynomial normalizing flows, where a neural network controls the parameters of the flow. In an empirical study with 3639 smart meter customers, our density predictions for 24h-ahead load forecasting compare favorably against Gaussian and Gaussian mixture densities. Furthermore, they outperform a non-parametric approach based on the pinball loss, especially in low-data scenarios.
Deep transformation models
(2021)
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks it is predominantly used to just predict a single number. This ignores the non-deterministic character of most tasks. Especially if crucial decisions are based on the predictions, like in medical applications, it is essential to quantify the prediction uncertainty. The presented deep learning transformation model estimates the whole conditional probability distribution, which is the most thorough way to capture uncertainty about the outcome. We combine ideas from a statistical transformation model (most likely transformation) with recent transformation models from deep learning (normalizing flows) to predict complex outcome distributions. The core of the method is a parameterized transformation function which can be trained with the usual maximum likelihood framework using gradient descent. The method can be combined with existing deep learning architectures. For small machine learning benchmark datasets, we report state of the art performance for most dataset and partly even outperform it. Our method works for complex input data, which we demonstrate by employing a CNN architecture on image data.