Sandesh Ghimire

Sandesh Ghimire, Jinyang Liu, Armand Comas et al.

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from noise are Wasserstein gradient flow in the space of probability measures. We are the first to prove this connection. Our understanding of Score-based (and Diffusion) generative models have matured and become more complete by drawing ideas from different fields like Bayesian inference, control theory, stochastic differential equation and Schrodinger bridge. However, many open questions and challenges remain. One problem, for example, is how to decrease the sampling time? We demonstrate that looking from geometric perspective enables us to answer many of these questions and provide new interpretations to some known results. Furthermore, geometric perspective enables us to devise an intuitive geometric solution to the problem of faster sampling. By augmenting traditional score-based generative models with a projection step, we show that we can generate high quality images with significantly fewer sampling-steps.

Nilesh Kumar, Prashnna K. Gyawali, Sandesh Ghimire et al.

Obtaining labelled data in medical image segmentation is challenging due to the need for pixel-level annotations by experts. Recent works have shown that augmenting the object of interest with deformable transformations can help mitigate this challenge. However, these transformations have been learned globally for the image, limiting their transferability across datasets or applicability in problems where image alignment is difficult. While object-centric augmentations provide a great opportunity to overcome these issues, existing works are only focused on position and random transformations without considering shape variations of the objects. To this end, we propose a novel object-centric data augmentation model that is able to learn the shape variations for the objects of interest and augment the object in place without modifying the rest of the image. We demonstrated its effectiveness in improving kidney tumour segmentation when leveraging shape variations learned both from within the same dataset and transferred from external datasets.

Prashnna Kumar Gyawali, Sandesh Ghimire, Linwei Wang

The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the behavior of the neural function on large unlabeled data. The smoothness of the neural function is a commonly used assumption exploited in SSL. A successful example is the adoption of mixup strategy in SSL that enforces the global smoothness of the neural function by encouraging it to behave linearly when interpolating between training examples. Despite its empirical success, however, the theoretical underpinning of how mixup regularizes the neural function has not been fully understood. In this paper, we offer a theoretically substantiated proposition that mixup improves the smoothness of the neural function by bounding the Lipschitz constant of the gradient function of the neural networks. We then propose that this can be strengthened by simultaneously constraining the Lipschitz constant of the neural function itself through adversarial Lipschitz regularization, encouraging the neural function to behave linearly while also constraining the slope of this linear function. On three benchmark data sets and one real-world biomedical data set, we demonstrate that this combined regularization results in improved generalization performance of SSL when learning from a small amount of labeled data. We further demonstrate the robustness of the presented method against single-step adversarial attacks. Our code is available at https://github.com/Prasanna1991/Mixup-LR.

Prashnna Kumar Gyawali, Sandesh Ghimire, Pradeep Bajracharya et al.

Computer-aided diagnosis via deep learning relies on large-scale annotated data sets, which can be costly when involving expert knowledge. Semi-supervised learning (SSL) mitigates this challenge by leveraging unlabeled data. One effective SSL approach is to regularize the local smoothness of neural functions via perturbations around single data points. In this work, we argue that regularizing the global smoothness of neural functions by filling the void in between data points can further improve SSL. We present a novel SSL approach that trains the neural network on linear mixing of labeled and unlabeled data, at both the input and latent space in order to regularize different portions of the network. We evaluated the presented model on two distinct medical image data sets for semi-supervised classification of thoracic disease and skin lesion, demonstrating its improved performance over SSL with local perturbations and SSL with global mixing but at the input space only. Our code is available at https://github.com/Prasanna1991/LatentMixing.

Sandesh Ghimire, Aria Masoomi, Jennifer Dy

Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable manner. However, we noted that most of these methods using neural network discriminators suffer from high fluctuations (variance) in estimates and instability in training. In this paper, we look at this issue from statistical learning theory and function space complexity perspective to understand why this happens and how to solve it. We argue that the cause of these pathologies is lack of control over the complexity of the neural network discriminator function and could be mitigated by controlling it. To achieve this objective, we 1) present a novel construction of the discriminator in the Reproducing Kernel Hilbert Space (RKHS), 2) theoretically relate the error probability bound of the KL estimates to the complexity of the discriminator in the RKHS space, 3) present a scalable way to control the complexity (RKHS norm) of the discriminator for a reliable estimation of KL divergence, and 4) prove the consistency of the proposed estimator. In three different applications of KL divergence : estimation of KL, estimation of mutual information and Variational Bayes, we show that by controlling the complexity as developed in the theory, we are able to reduce the variance of KL estimates and stabilize the training

Xiajun Jiang, Sandesh Ghimire, Jwala Dhamala et al.

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper, we present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph over the graphical embedding of the two geometry. We applied the presented network to reconstructing electrical activity on the heart surface from body-surface potential. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the presented network to generalize across geometrical changes underlying the data in comparison to its Euclidean alternatives.

Sandesh Ghimire, Prashnna K Gyawali, Linwei Wang

Several scalable sample-based methods to compute the Kullback Leibler (KL) divergence between two distributions have been proposed and applied in large-scale machine learning models. While they have been found to be unstable, the theoretical root cause of the problem is not clear. In this paper, we study a generative adversarial network based approach that uses a neural network discriminator to estimate KL divergence. We argue that, in such case, high fluctuations in the estimates are a consequence of not controlling the complexity of the discriminator function space. We provide a theoretical underpinning and remedy for this problem by first constructing a discriminator in the Reproducing Kernel Hilbert Space (RKHS). This enables us to leverage sample complexity and mean embedding to theoretically relate the error probability bound of the KL estimates to the complexity of the discriminator in RKHS. Based on this theory, we then present a scalable way to control the complexity of the discriminator for a reliable estimation of KL divergence. We support both our proposed theory and method to control the complexity of the RKHS discriminator through controlled experiments.

Prashnna Kumar Gyawali, Zhiyuan Li, Cameron Knight et al.

To improve the ability of VAE to disentangle in the latent space, existing works mostly focus on enforcing independence among the learned latent factors. However, the ability of these models to disentangle often decreases as the complexity of the generative factors increases. In this paper, we investigate the little-explored effect of the modeling capacity of a posterior density on the disentangling ability of the VAE. We note that the independence within and the complexity of the latent density are two different properties we constrain when regularizing the posterior density: while the former promotes the disentangling ability of VAE, the latter -- if overly limited -- creates an unnecessary competition with the data reconstruction objective in VAE. Therefore, if we preserve the independence but allow richer modeling capacity in the posterior density, we will lift this competition and thereby allow improved independence and data reconstruction at the same time. We investigate this theoretical intuition with a VAE that utilizes a non-parametric latent factor model, the Indian Buffet Process (IBP), as a latent density that is able to grow with the complexity of the data. Across three widely-used benchmark data sets and two clinical data sets little explored for disentangled learning, we qualitatively and quantitatively demonstrated the improved disentangling performance of IBP-VAE over the state of the art. In the latter two clinical data sets riddled with complex factors of variations, we further demonstrated that unsupervised disentangling of nuisance factors via IBP-VAE -- when combined with a supervised objective -- can not only improve task accuracy in comparison to relevant supervised deep architectures but also facilitate knowledge discovery related to task decision-making. A shorter version of this work will appear in the ICDM 2019 conference proceedings.

Prashnna Kumar Gyawali, Zhiyuan Li, Sandesh Ghimire et al.

The success of deep learning in medical imaging is mostly achieved at the cost of a large labeled data set. Semi-supervised learning (SSL) provides a promising solution by leveraging the structure of unlabeled data to improve learning from a small set of labeled data. Self-ensembling is a simple approach used in SSL to encourage consensus among ensemble predictions of unknown labels, improving generalization of the model by making it more insensitive to the latent space. Currently, such an ensemble is obtained by randomization such as dropout regularization and random data augmentation. In this work, we hypothesize -- from the generalization perspective -- that self-ensembling can be improved by exploiting the stochasticity of a disentangled latent space. To this end, we present a stacked SSL model that utilizes unsupervised disentangled representation learning as the stochastic embedding for self-ensembling. We evaluate the presented model for multi-label classification using chest X-ray images, demonstrating its improved performance over related SSL models as well as the interpretability of its disentangled representations.

Sandesh Ghimire, Jwala Dhamala, Prashnna Kumar Gyawali et al.

Noninvasive reconstruction of cardiac transmembrane potential (TMP) from surface electrocardiograms (ECG) involves an ill-posed inverse problem. Model-constrained regularization is powerful for incorporating rich physiological knowledge about spatiotemporal TMP dynamics. These models are controlled by high-dimensional physical parameters which, if fixed, can introduce model errors and reduce the accuracy of TMP reconstruction. Simultaneous adaptation of these parameters during TMP reconstruction, however, is difficult due to their high dimensionality. We introduce a novel model-constrained inference framework that replaces conventional physiological models with a deep generative model trained to generate TMP sequences from low-dimensional generative factors. Using a variational auto-encoder (VAE) with long short-term memory (LSTM) networks, we train the VAE decoder to learn the conditional likelihood of TMP, while the encoder learns the prior distribution of generative factors. These two components allow us to develop an efficient algorithm to simultaneously infer the generative factors and TMP signals from ECG data. Synthetic and real-data experiments demonstrate that the presented method significantly improve the accuracy of TMP reconstruction compared with methods constrained by conventional physiological models or without physiological constraints.

Sandesh Ghimire, Prashnna Kumar Gyawali, Jwala Dhamala et al.

Deep learning networks have shown state-of-the-art performance in many image reconstruction problems. However, it is not well understood what properties of representation and learning may improve the generalization ability of the network. In this paper, we propose that the generalization ability of an encoder-decoder network for inverse reconstruction can be improved in two means. First, drawing from analytical learning theory, we theoretically show that a stochastic latent space will improve the ability of a network to generalize to test data outside the training distribution. Second, following the information bottleneck principle, we show that a latent representation minimally informative of the input data will help a network generalize to unseen input variations that are irrelevant to the output reconstruction. Therefore, we present a sequence image reconstruction network optimized by a variational approximation of the information bottleneck principle with stochastic latent space. In the application setting of reconstructing the sequence of cardiac transmembrane potential from bodysurface potential, we assess the two types of generalization abilities of the presented network against its deterministic counterpart. The results demonstrate that the generalization ability of an inverse reconstruction network can be improved by stochasticity as well as the information bottleneck.

Prashnna K Gyawali, Cameron Knight, Sandesh Ghimire et al.

While deep representation learning has become increasingly capable of separating task-relevant representations from other confounding factors in the data, two significant challenges remain. First, there is often an unknown and potentially infinite number of confounding factors coinciding in the data. Second, not all of these factors are readily observable. In this paper, we present a deep conditional generative model that learns to disentangle a task-relevant representation from an unknown number of confounding factors that may grow infinitely. This is achieved by marrying the representational power of deep generative models with Bayesian non-parametric factor models, where a supervised deterministic encoder learns task-related representation and a probabilistic encoder with an Indian Buffet Process (IBP) learns the unknown number of unobservable confounding factors. We tested the presented model in two datasets: a handwritten digit dataset (MNIST) augmented with colored digits and a clinical ECG dataset with significant inter-subject variations and augmented with signal artifacts. These diverse data sets highlighted the ability of the presented model to grow with the complexity of the data and identify the absence or presence of unobserved confounding factors.

Sandesh Ghimire, Prashnna Kumar Gyawali, John L Sapp et al.

Deep learning models have shown state-of-the-art performance in many inverse reconstruction problems. However, it is not well understood what properties of the latent representation may improve the generalization ability of the network. Furthermore, limited models have been presented for inverse reconstructions over time sequences. In this paper, we study the generalization ability of a sequence encoder decoder model for solving inverse reconstructions on time sequences. Our central hypothesis is that the generalization ability of the network can be improved by 1) constrained stochasticity and 2) global aggregation of temporal information in the latent space. First, drawing from analytical learning theory, we theoretically show that a stochastic latent space will lead to an improved generalization ability. Second, we consider an LSTM encoder-decoder architecture that compresses a global latent vector from all last-layer units in the LSTM encoder. This model is compared with alternative LSTM encoder-decoder architectures, each in deterministic and stochastic versions. The results demonstrate that the generalization ability of an inverse reconstruction network can be improved by constrained stochasticity combined with global aggregation of temporal information in the latent space.