Reliable probability estimation is of crucial importance in many real-world applications where there is inherent uncertainty, such as weather forecasting, medical prognosis, or collision avoidance in autonomous vehicles. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the important difference that the objective is to estimate probabilities rather than predicting the specific outcome. The goal of this work is to investigate probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on classification problems where the probabilities are related to model uncertainty. In the case of problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. Finally, we also propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Denoising is a fundamental challenge in scientific imaging. Deep convolutional neural networks (CNNs) provide the current state of the art in denoising natural images, where they produce impressive results. However, their potential has barely been explored in the context of scientific imaging. Denoising CNNs are typically trained on real natural images artificially corrupted with simulated noise. In contrast, in scientific applications, noiseless ground-truth images are usually not available. To address this issue, we propose a simulation-based denoising (SBD) framework, in which CNNs are trained on simulated images. We test the framework on data obtained from transmission electron microscopy (TEM), an imaging technique with widespread applications in material science, biology, and medicine. SBD outperforms existing techniques by a wide margin on a simulated benchmark dataset, as well as on real data. Apart from the denoised images, SBD generates likelihood maps to visualize the agreement between the structure of the denoised image and the observed data. Our results reveal shortcomings of state-of-the-art denoising architectures, such as their small field-of-view: substantially increasing the field-of-view of the CNNs allows them to exploit non-local periodic patterns in the data, which is crucial at high noise levels. In addition, we analyze the generalization capability of SBD, demonstrating that the trained networks are robust to variations of imaging parameters and of the underlying signal structure. Finally, we release the first publicly available benchmark dataset of TEM images, containing 18,000 examples.

Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve robustness. For ConvNets, most existing methods are based on penalizing or normalizing weight matrices derived from concatenating or flattening the convolutional kernels. These methods often destroy or ignore the benign convolutional structure of the kernels; therefore, they are often expensive or impractical for deep ConvNets. In contrast, we introduce a simple and efficient ``convolutional normalization'' method that can fully exploit the convolutional structure in the Fourier domain and serve as a simple plug-and-play module to be conveniently incorporated into any ConvNets. Our method is inspired by recent work on preconditioning methods for convolutional sparse coding and can effectively promote each layer's channel-wise isometry. Furthermore, we show that convolutional normalization can reduce the layerwise spectral norm of the weight matrices and hence improve the Lipschitzness of the network, leading to easier training and improved robustness for deep ConvNets. Applied to classification under noise corruptions and generative adversarial network (GAN), we show that convolutional normalization improves the robustness of common ConvNets such as ResNet and the performance of GAN. We verify our findings via extensive numerical experiments on CIFAR-10, CIFAR-100, and ImageNet.

Deep convolutional neural networks (CNNs) currently achieve state-of-the-art performance in denoising videos. They are typically trained with supervision, minimizing the error between the network output and ground-truth clean videos. However, in many applications, such as microscopy, noiseless videos are not available. To address these cases, we build on recent advances in unsupervised still image denoising to develop an Unsupervised Deep Video Denoiser (UDVD). UDVD is shown to perform competitively with current state-of-the-art supervised methods on benchmark datasets, even when trained only on a single short noisy video sequence. Experiments on fluorescence-microscopy and electron-microscopy data illustrate the promise of our approach for imaging modalities where ground-truth clean data is generally not available. In addition, we study the mechanisms used by trained CNNs to perform video denoising. An analysis of the gradient of the network output with respect to its input reveals that these networks perform spatio-temporal filtering that is adapted to the particular spatial structures and motion of the underlying content. We interpret this as an implicit and highly effective form of motion compensation, a widely used paradigm in traditional video denoising, compression, and analysis. Code and iPython notebooks for our analysis are available in https://sreyas-mohan.github.io/udvd/ .

We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classification tasks, which exploits the progress of the early learning phase. In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization. There are two key elements to our approach. First, we leverage semi-supervised learning techniques to produce target probabilities based on the model outputs. Second, we design a regularization term that steers the model towards these targets, implicitly preventing memorization of the false labels. The resulting framework is shown to provide robustness to noisy annotations on several standard benchmarks and real-world datasets, where it achieves results comparable to the state of the art.

Recovery after stroke is often incomplete, but rehabilitation training may potentiate recovery by engaging endogenous neuroplasticity. In preclinical models of stroke, high doses of rehabilitation training are required to restore functional movement to the affected limbs of animals. In humans, however, the necessary dose of training to potentiate recovery is not known. This ignorance stems from the lack of objective, pragmatic approaches for measuring training doses in rehabilitation activities. Here, to develop a measurement approach, we took the critical first step of automatically identifying functional primitives, the basic building block of activities. Forty-eight individuals with chronic stroke performed a variety of rehabilitation activities while wearing inertial measurement units (IMUs) to capture upper body motion. Primitives were identified by human labelers, who labeled and segmented the associated IMU data. We performed automatic classification of these primitives using machine learning. We designed a convolutional neural network model that outperformed existing methods. The model includes an initial module to compute separate embeddings of different physical quantities in the sensor data. In addition, it replaces batch normalization (which performs normalization based on statistics computed from the training data) with instance normalization (which uses statistics computed from the test data). This increases robustness to possible distributional shifts when applying the method to new patients. With this approach, we attained an average classification accuracy of 70%. Thus, using a combination of IMU-based motion capture and deep learning, we were able to identify primitives automatically. This approach builds towards objectively-measured rehabilitation training, enabling the identification and counting of functional primitives that accrues to a training dose.

Extraneous variables are variables that are irrelevant for a certain task, but heavily affect the distribution of the available data. In this work, we show that the presence of such variables can degrade the performance of deep-learning models. We study three datasets where there is a strong influence of known extraneous variables: classification of upper-body movements in stroke patients, annotation of surgical activities, and recognition of corrupted images. Models trained with batch normalization learn features that are highly dependent on the extraneous variables. In batch normalization, the statistics used to normalize the features are learned from the training set and fixed at test time, which produces a mismatch in the presence of varying extraneous variables. We demonstrate that estimating the feature statistics adaptively during inference, as in instance normalization, addresses this issue, producing normalized features that are more robust to changes in the extraneous variables. This results in a significant gain in performance for different network architectures and choices of feature statistics.

Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over batches of training images (a component of "batch normalization"). Recent state-of-the-art blind denoising methods (e.g., DnCNN) seem to require these terms for their success. Here, however, we show that these networks systematically overfit the noise levels for which they are trained: when deployed at noise levels outside the training range, performance degrades dramatically. In contrast, a bias-free architecture -- obtained by removing the constant terms in every layer of the network, including those used for batch normalization-- generalizes robustly across noise levels, while preserving state-of-the-art performance within the training range. Locally, the bias-free network acts linearly on the noisy image, enabling direct analysis of network behavior via standard linear-algebraic tools. These analyses provide interpretations of network functionality in terms of nonlinear adaptive filtering, and projection onto a union of low-dimensional subspaces, connecting the learning-based method to more traditional denoising methodology.

Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal signal from a finite number of noisy samples. A recent machine-learning approach uses a neural network to output a learned representation with local maxima at the position of the frequency estimates. In this work, we propose a novel neural-network architecture that produces a significantly more accurate representation, and combine it with an additional neural-network module trained to detect the number of frequencies. This yields a fast, fully-automatic method for frequency estimation that achieves state-of-the-art results. In particular, it outperforms existing techniques by a substantial margin at medium-to-high noise levels.

We propose a nonparametric model for time series with missing data based on low-rank matrix factorization. The model expresses each instance in a set of time series as a linear combination of a small number of shared basis functions. Constraining the functions and the corresponding coefficients to be nonnegative yields an interpretable low-dimensional representation of the data. A time-smoothing regularization term ensures that the model captures meaningful trends in the data, instead of overfitting short-term fluctuations. The low-dimensional representation makes it possible to detect outliers and cluster the time series according to the interpretable features extracted by the model, and also to perform forecasting via kernel regression. We apply our methodology to a large real-world dataset of infant-sleep data gathered by caregivers with a mobile-phone app. Our analysis automatically extracts daily-sleep patterns consistent with the existing literature. This allows us to compute sleep-development trends for the cohort, which characterize the emergence of circadian sleep and different napping habits. We apply our methodology to detect anomalous individuals, to cluster the cohort into groups with different sleeping tendencies, and to obtain improved predictions of future sleep behavior.