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Understanding the role of regularization is a central question in Statistical Inference. Empirically, well-chosen regularization schemes often dramatically improve the quality of the inferred models by avoiding overfitting of the training data. We consider here the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models. Based on analytical calculations on Gaussian multivariate distributions and numerical experiments on Gaussian and Potts models we study the likelihoods of the training, test, and 'generated data' (with the inferred models) sets as functions of the regularization strengths. We show in particular that, at its maximum, the test likelihood and the 'generated' likelihood, which quantifies the quality of the generated samples, have remarkably close values. The optimal value for the regularization strength is found to be approximately equal to the inverse sum of the squared couplings incoming on sites on the underlying network of interactions. Our results seem largely independent of the structure of the true underlying interactions that generated the data, of the regularization scheme considered, and are valid when small fluctuations of the posterior distribution around the MAP estimator are taken into account. Connections with empirical works on protein models learned from homologous sequences are discussed.

In this note we consider non-stationary cluster point processes and we derive their conditional intensity, i.e. the intensity of the process given the locations of one or more events of the process. We then provide some approximations of the conditional intensity.

An important propertyfor deep neural networks to possess is the ability to perform robust out of distribution detection (OOD) on previously unseen data. This property is essential for safety purposes when deploying models for real world applications. Recent studies show that probabilistic generative models can perform poorly on this task, which is surprising given that they seek to estimate the likelihood of training data. To alleviate this issue, we propose the exponentially tilted Gaussian prior distribution for the Variational Autoencoder (VAE). With this prior, we are able to achieve state-of-the art results using just the negative log likelihood that the VAE naturally assigns, while being orders of magnitude faster than some competitive methods. We also show that our model produces high quality image samples which are more crisp than that of a standard Gaussian VAE. The new prior distribution has a very simple implementation which uses a Kullback Leibler divergence that compares the difference between a latent vector's length, and the radius of a sphere.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

This work presents a new strategy for multi-class classification that requires no class-specific labels, but instead leverages pairwise similarity between examples, which is a weaker form of annotation. The proposed method, meta classification learning, optimizes a binary classifier for pairwise similarity prediction and through this process learns a multi-class classifier as a submodule. We formulate this approach, present a probabilistic graphical model for it, and derive a surprisingly simple loss function that can be used to learn neural network-based models. We then demonstrate that this same framework generalizes to the supervised, unsupervised cross-task, and semi-supervised settings. Our method is evaluated against state of the art in all three learning paradigms and shows a superior or comparable accuracy, providing evidence that learning multi-class classification without multi-class labels is a viable learning option.

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.

In machine learning, novelty detection is the task of identifying novel unseen data. During training, only samples from the normal class are available. Test samples are classified as normal or abnormal by assignment of a novelty score. Here we propose novelty detection methods based on training variational autoencoders (VAEs) on normal data. Since abnormal samples are not used during training, we define novelty metrics based on the (partially complementary) assumptions that the VAE is less capable of reconstructing abnormal samples well; that abnormal samples more strongly violate the VAE regularizer; and that abnormal samples differ from normal samples not only in input-feature space, but also in the VAE latent space and VAE output. These approaches, combined with various possibilities of using (e.g. sampling) the probabilistic VAE to obtain scalar novelty scores, yield a large family of methods. We apply these methods to magnetic resonance imaging, namely to the detection of diffusion-space (q-space) abnormalities in diffusion MRI scans of multiple sclerosis patients, i.e. to detect multiple sclerosis lesions without using any lesion labels for training. Many of our methods outperform previously proposed q-space novelty detection methods. We also evaluate the proposed methods on the MNIST handwritten digits dataset and show that many of them are able to outperform the state of the art.

We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned with the underlying generative factors of variation of data emerge when optimising the modified ELBO bound in $\beta$-VAE, as training progresses. From these insights, we propose a modification to the training regime of $\beta$-VAE, that progressively increases the information capacity of the latent code during training. This modification facilitates the robust learning of disentangled representations in $\beta$-VAE, without the previous trade-off in reconstruction accuracy.

We investigate deep generative models that can exchange multiple modalities bi-directionally, e.g., generating images from corresponding texts and vice versa. A major approach to achieve this objective is to train a model that integrates all the information of different modalities into a joint representation and then to generate one modality from the corresponding other modality via this joint representation. We simply applied this approach to variational autoencoders (VAEs), which we call a joint multimodal variational autoencoder (JMVAE). However, we found that when this model attempts to generate a large dimensional modality missing at the input, the joint representation collapses and this modality cannot be generated successfully. Furthermore, we confirmed that this difficulty cannot be resolved even using a known solution. Therefore, in this study, we propose two models to prevent this difficulty: JMVAE-kl and JMVAE-h. Results of our experiments demonstrate that these methods can prevent the difficulty above and that they generate modalities bi-directionally with equal or higher likelihood than conventional VAE methods, which generate in only one direction. Moreover, we confirm that these methods can obtain the joint representation appropriately, so that they can generate various variations of modality by moving over the joint representation or changing the value of another modality.