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Despite the tremendous empirical success of deep learning models to solve various learning tasks, our theoretical understanding of their generalization ability is very limited. Classical generalization bounds based on tools such as the VC dimension or Rademacher complexity, are so far unsuitable for deep models and it is doubtful that these techniques can yield tight bounds even in the most idealistic settings (Nagarajan & Kolter, 2019). In this work, we instead revisit the concept of leave-one-out (LOO) error to measure the generalization ability of deep models in the so-called kernel regime. While popular in statistics, the LOO error has been largely overlooked in the context of deep learning. By building upon the recently established connection between neural networks and kernel learning, we leverage the closed-form expression for the leave-one-out error, giving us access to an efficient proxy for the test error. We show both theoretically and empirically that the leave-one-out error is capable of capturing various phenomena in generalization theory, such as double descent, random labels or transfer learning. Our work therefore demonstrates that the leave-one-out error provides a tractable way to estimate the generalization ability of deep neural networks in the kernel regime, opening the door to potential, new research directions in the field of generalization.

Dark matter in the universe evolves through gravity to form a complex network of halos, filaments, sheets and voids, that is known as the cosmic web. Computational models of the underlying physical processes, such as classical N-body simulations, are extremely resource intensive, as they track the action of gravity in an expanding universe using billions of particles as tracers of the cosmic matter distribution. Therefore, upcoming cosmology experiments will face a computational bottleneck that may limit the exploitation of their full scientific potential. To address this challenge, we demonstrate the application of a machine learning technique called Generative Adversarial Networks (GAN) to learn models that can efficiently generate new, physically realistic realizations of the cosmic web. Our training set is a small, representative sample of 2D image snapshots from N-body simulations of size 500 and 100 Mpc. We show that the GAN-generated samples are qualitatively and quantitatively very similar to the originals. For the larger boxes of size 500 Mpc, it is very difficult to distinguish them visually. The agreement of the power spectrum Pk is 1–2% for most of the range, between k=0.06 and k=0.4. For the remaining values of k, the agreement is within 15%, with the error rate increasing for k>0.8. For smaller boxes of size 100 Mpc, we find that the visual agreement to be good, but some differences are noticable. The error on the power spectrum is of the order of 20%. We attribute this loss of performance to the fact that the matter distribution in 100 Mpc cutouts was very inhomogeneous between images, a situation in which the performance of GANs is known to deteriorate. We find a good match for the correlation matrix of full Pk range for 100 Mpc data and of small scales for 500 Mpc, with ∼20% disagreement for large scales. An important advantage of generating cosmic web realizations with a GAN is the considerable gains in terms of computation time. Each new sample generated by a GAN takes a fraction of a second, compared to the many hours needed by traditional N-body techniques. We anticipate that the use of generative models such as GANs will therefore play an important role in providing extremely fast and precise simulations of cosmic web in the era of large cosmological surveys, such as Euclid and Large Synoptic Survey Telescope (LSST)., Computational Astrophysics and Cosmology, 5, ISSN:2197-7909

During typical field campaigns, millions of cloud particle images are captured with imaging probes. Our interest lies in classifying these particles in order to compute the statistics needed for understanding clouds. Given the large volume of collected data, this raises the need for an automated classification approach. Traditional classification methods that require extracting features manually (e.g., decision trees and support vector machines) show reasonable performance when trained and tested on data coming from a unique dataset. However, they often have difficulties in generalizing to test sets coming from other datasets where the distribution of the features might be significantly different. In practice, we found that for holographic imagers each new dataset requires labeling a huge amount of data by hand using those methods. Convolutional neural networks have the potential to overcome this problem due to their ability to learn complex nonlinear models directly from the images instead of pre-engineered features, as well as by relying on powerful regularization techniques. We show empirically that a convolutional neural network trained on cloud particles from holographic imagers generalizes well to unseen datasets. Moreover, fine tuning the same network with a small number (256) of training images improves the classification accuracy. Thus, the automated classification with a convolutional neural network not only reduces the hand-labeling effort for new datasets but is also no longer the main error source for the classification of small particles., Atmospheric Measurement Techniques, 13 (5), ISSN:1867-1381, ISSN:1867-8548

Weak gravitational lensing mass maps play a crucial role in understanding the evolution of structures in the Universe and our ability to constrain cosmological models. The prediction of these mass maps is based on expensive N-body simulations, which can create a computational bottleneck for cosmological analyses. Simulation-based emulators of map summary statistics, such as the matter power spectrum and its covariance, are starting to play increasingly important role, as the analytical predictions are expected to reach their precision limits for upcoming experiments. Creating an emulator of the cosmological mass maps themselves, rather than their summary statistics, is a more challenging task. Modern deep generative models, such as Generative Adversarial Networks (GAN), have demonstrated their potential to achieve this goal. Most existing GAN approaches produce simulations for a fixed value of the cosmological parameters, which limits their practical applicability. We propose a novel conditional GAN model that is able to generate mass maps for any pair of matter density Ωm and matter clustering strength σ8, parameters which have the largest impact on the evolution of structures in the Universe, for a given source galaxy redshift distribution n(z). Our results show that our conditional GAN can interpolate efficiently within the space of simulated cosmologies, and generate maps anywhere inside this space with good visual quality high statistical accuracy. We perform an extensive quantitative comparison of the N-body and GAN -generated maps using a range of metrics: the pixel histograms, peak counts, power spectra, bispectra, Minkowski functionals, correlation matrices of the power spectra, the Multi-Scale Structural Similarity Index (MS-SSIM) and our equivalent of the Fréchet Inception Distance. We find a very good agreement on these metrics, with typical differences are, Frontiers in Artificial Intelligence, 4, ISSN:2624-8212

Proceedings of Machine Learning Research, 70, ISSN:2640-3498, Proceedings of the 34th International Conference on Machine Learning (ICML 2017)

We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we propose instead to use more flexible code distributions. These distributions are estimated non-parametrically by reversing the generator map during training. The benefits include: more powerful generative models, better modeling of latent structure and explicit control of the degree of generalization.

Segmenting images is a significant challenge that has drawn a lot of attention from different fields of artificial intelligence and has many practical applications. One such challenge addressed in this thesis is the segmentation of electron microscope (EM) imaging of neural tissue. EM microscopy is one of the key tools used to analyze neural tissue and understand the brain, but the huge amounts of data it produces make automated analysis necessary. In addition to the challenges specific to EM data, the common problems encountered in image segmentation must also be addressed. These problems include extracting discriminative features from the data and constructing a statistical model using ground-truth data. Although complex models appear to be more attractive because they allow for more expressiveness, they also lead to a higher computational complexity. On the other hand, simple models come with a lower complexity but less faithfully express the real world. Therefore, one of the most challenging tasks in image segmentation is in constructing models that are expressive enough while remaining tractable. In this work, we propose several automated graph partitioning approaches that address these issues. These methods reduce the computational complexity by operating on supervoxels instead of voxels, incorporating features capable of describing the 3D shape of the target objects and using structured models to account for correlation in output variables. One of the non-trivial issues with such models is that their parameters must be carefully chosen for optimal performance. A popular approach to learning model parameters is a maximum-margin approach called Structured SVM (SSVM) that provides optimality guarantees but also suffers from two main drawbacks. First, SSVM-based approaches are usually limited to linear kernels, since more powerful nonlinear kernels cause the learning to become prohibitively expensive. In this thesis, we introduce an approach to “kernelize” the features so that a linear SSVM framework can leverage the power of nonlinear kernels without incurring their high computational cost. Second, the optimality guarentees are violated for complex models with strong inter-relations between the output variables. We propose a new subgradient-based method that is more robust and leads to improved convergence properties and increased reliability. The different approaches presented in this thesis are applicable to both natural and medical images. They are able to segment mitochondria at a performance level close to that of a human annotator, and outperform state-of-the-art segmentation techniques while still benefiting from a low learning time.

Superpixels are becoming increasingly popular for use in computer vision applications. However, there are few algorithms that output a desired number of regular, compact superpixels with a low computational overhead. We introduce a novel algorithm that clusters pixels in the combined five-dimensional color and image plane space to efficiently generate compact, nearly uniform superpixels. The simplicity of our approach makes it extremely easy to use -- a lone parameter specifies the number of superpixels -- and the efficiency of the algorithm makes it very practical. Experiments show that our approach produces superpixels at a lower computational cost while achieving a segmentation quality equal to or greater than four state-of-the-art methods, as measured by boundary recall and under-segmentation error. We also demonstrate the benefits of our superpixel approach in contrast to existing methods for two tasks in which superpixels have already been shown to increase performance over pixel-based methods.

Immense amounts of high resolution data are now routinely produced thanks to recent advances in EM imaging. While a strong demand for automated analysis now exists, it is stifled by the lack of robust automatic 3D segmentation techniques. State-of-the-art Computer Vision algorithms designed to operate on natural 2D images tend to perform poorly when applied to EM image stacks for a number of reasons. The sheer size of a typical EM image stack renders many segmentation schemes intractable. Most approaches rely on local statistics that easily become confused when confronted with the noise and textures found within EM image stacks. The assumption that strong image gradients always correspond to object boundaries is violated by cluttered membranes belonging to numerous objects. In this work, we propose an automated graph partitioning scheme that addresses these issues. It reduces the computational complexity by operating on supervoxels instead of voxels, incorporates global shape features capable of describing the 3D shape of the target objects, and learns to recognize the distinctive appearance of true boundaries. Our experiments demonstrate that, when applied to segment mitochondria from neural tissue, our approach closely matches the performance of human annotators and outperforms a state-of-the-art 3D segmentation technique.