This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced visualizations of the dataset as well as very distinct clusterizations. It is also faster than similar clusterization methods that are sensitive to density and shapes such as Mitosis and TRICLUST. In addition, k-MS is deterministic and has an intrinsic sense of maximal clusters that can be created for a given input sample and input parameters, differing from k-Means and other clusterization algorithms. In other words, given a constant k, a structuring element and a dataset, k-MS produces k or less clusters without using random/ pseudo-random functions. Finally, the proposed algorithm also provides a straightforward means for removing noise from images or datasets in general.

What would it take for a natural language model to understand a novel, such as The Lord of the Rings? Among other things, such a model must be able to: (a) identify and record new characters (entities) and their attributes as they are introduced in the text, and (b) identify subsequent references to the characters previously introduced and update their attributes. This problem of entity tracking is essential for language understanding, and thus, useful for a wide array of downstream applications in NLP such as question-answering, summarization. In this thesis, we focus on two key problems in relation to facilitating the use of entity tracking models: (i) scaling entity tracking models to long documents, such as a novel, and (ii) integrating entity tracking into language models. Applying language technologies to long documents has garnered interest recently, but computational constraints are a significant bottleneck in scaling up current methods. In this thesis, we argue that computationally efficient entity tracking models can be developed by representing entities with rich, fixed-dimensional vector representations derived from pretrained language models, and by exploiting the ephemeral nature of entities. We also argue for the integration of entity tracking into language models as it will allow for: (i) wider application given the current ubiquitous use of pretrained language models in NLP applications, and (ii) easier adoption since it is much easier to swap in a new pretrained language model than to integrate a separate standalone entity tracking model.

This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not excluding even more general objects such as time series or spatial point patterns. As a generative model for such data, we introduce a stochastic block model with a general measurable interaction space $\mathcal S$, for which we derive information-theoretic bounds for the minimum achievable error rate. These bounds yield sharp criteria for the existence of consistent and strongly consistent estimators in terms of data sparsity, statistical similarity between intra- and inter-block interaction distributions, and the shape and size of the interaction space. The general framework makes it possible to study temporal and multiplex networks with $\mathcal S = \{0,1\}^T$, in settings where both $N \to \infty$ and $T \to \infty$, and the temporal interaction patterns are correlated over time. For temporal Markov interactions, we derive sharp consistency thresholds. We also present fast online estimation algorithms which fully utilise the non-binary nature of the observed data. Numerical experiments on synthetic and real data show that these algorithms rapidly produce accurate estimates even for very sparse data arrays.

Objective: Disease knowledge graphs are a way to connect, organize, and access disparate information about diseases with numerous benefits for artificial intelligence (AI). To create knowledge graphs, it is necessary to extract knowledge from multimodal datasets in the form of relationships between disease concepts and normalize both concepts and relationship types. Methods: We introduce REMAP, a multimodal approach for disease relation extraction and classification. The REMAP machine learning approach jointly embeds a partial, incomplete knowledge graph and a medical language dataset into a compact latent vector space, followed by aligning the multimodal embeddings for optimal disease relation extraction. Results: We apply REMAP approach to a disease knowledge graph with 96,913 relations and a text dataset of 1.24 million sentences. On a dataset annotated by human experts, REMAP improves text-based disease relation extraction by 10.0% (accuracy) and 17.2% (F1-score) by fusing disease knowledge graphs with text information. Further, REMAP leverages text information to recommend new relationships in the knowledge graph, outperforming graph-based methods by 8.4% (accuracy) and 10.4% (F1-score). Conclusion: REMAP is a multimodal approach for extracting and classifying disease relationships by fusing structured knowledge and text information. REMAP provides a flexible neural architecture to easily find, access, and validate AI-driven relationships between disease concepts.

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can perform poorly, leading to work in metric learning. However, being able to learn a similarity-sensitive distance function also presupposes access to a rich, discriminative representation for the objects at hand. In this dissertation we present contributions towards both ends. In the first part of the thesis, assuming good representations for the data, we present a formulation for metric learning that makes a more direct attempt to optimize for the k-NN accuracy as compared to prior work. We also present extensions of this formulation to metric learning for kNN regression, asymmetric similarity learning and discriminative learning of Hamming distance. In the second part, we consider a situation where we are on a limited computational budget i.e. optimizing over a space of possible metrics would be infeasible, but access to a label aware distance metric is still desirable. We present a simple, and computationally inexpensive approach for estimating a well motivated metric that relies only on gradient estimates, discussing theoretical and experimental results. In the final part, we address representational issues, considering group equivariant convolutional neural networks (GCNNs). Equivariance to symmetry transformations is explicitly encoded in GCNNs; a classical CNN being the simplest example. In particular, we present a SO(3)-equivariant neural network architecture for spherical data, that operates entirely in Fourier space, while also providing a formalism for the design of fully Fourier neural networks that are equivariant to the action of any continuous compact group.

The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix, either directly or implicitly. In this work, we introduce a network embedding method from a new perspective, which leverages Modern Hopfield Networks (MHN) for associative learning. Our network learns associations between the content of each node and that node's neighbors. These associations serve as memories in the MHN. The recurrent dynamics of the network make it possible to recover the masked node, given that node's neighbors. Our proposed method is evaluated on different downstream tasks such as node classification and linkage prediction. The results show competitive performance compared to the common matrix factorization techniques and deep learning based methods.

Deep neural networks have achieved impressive results in many image classification tasks. However, since their performance is usually measured in controlled settings, it is important to ensure that their decisions remain correct when deployed in noisy environments. In fact, deep networks are not robust to a large variety of semantic-preserving image modifications, even to imperceptible image changes known as adversarial perturbations. The poor robustness of image classifiers to small data distribution shifts raises serious concerns regarding their trustworthiness. To build reliable machine learning models, we must design principled methods to analyze and understand the mechanisms that shape robustness and invariance. This is exactly the focus of this thesis. First, we study the problem of computing sparse adversarial perturbations. We exploit the geometry of the decision boundaries of image classifiers for computing sparse perturbations very fast, and reveal a qualitative connection between adversarial examples and the data features that image classifiers learn. Then, to better understand this connection, we propose a geometric framework that connects the distance of data samples to the decision boundary, with the features existing in the data. We show that deep classifiers have a strong inductive bias towards invariance to non-discriminative features, and that adversarial training exploits this property to confer robustness. Finally, we focus on the challenging problem of generalization to unforeseen corruptions of the data, and we propose a novel data augmentation scheme for achieving state-of-the-art robustness to common corruptions of the images. Overall, our results contribute to the understanding of the fundamental mechanisms of deep image classifiers, and pave the way for building more reliable machine learning systems that can be deployed in real-world environments.

We demonstrate an end-to-end framework to improve the resilience of man-made systems to unforeseen events. The framework is based on a physics-based digital twin model and three modules tasked with real-time fault diagnosis, prognostics and reconfiguration. The fault diagnosis module uses model-based diagnosis algorithms to detect and isolate faults and generates interventions in the system to disambiguate uncertain diagnosis solutions. We scale up the fault diagnosis algorithm to the required real-time performance through the use of parallelization and surrogate models of the physics-based digital twin. The prognostics module tracks the fault progressions and trains the online degradation models to compute remaining useful life of system components. In addition, we use the degradation models to assess the impact of the fault progression on the operational requirements. The reconfiguration module uses PDDL-based planning endowed with semantic attachments to adjust the system controls so that the fault impact on the system operation is minimized. We define a resilience metric and use the example of a fuel system model to demonstrate how the metric improves with our framework.

Cryo-electron microscopy (cryo-EM) has become a tool of fundamental importance in structural biology, helping us understand the basic building blocks of life. The algorithmic challenge of cryo-EM is to jointly estimate the unknown 3D poses and the 3D electron scattering potential of a biomolecule from millions of extremely noisy 2D images. Existing reconstruction algorithms, however, cannot easily keep pace with the rapidly growing size of cryo-EM datasets due to their high computational and memory cost. We introduce cryoAI, an ab initio reconstruction algorithm for homogeneous conformations that uses direct gradient-based optimization of particle poses and the electron scattering potential from single-particle cryo-EM data. CryoAI combines a learned encoder that predicts the poses of each particle image with a physics-based decoder to aggregate each particle image into an implicit representation of the scattering potential volume. This volume is stored in the Fourier domain for computational efficiency and leverages a modern coordinate network architecture for memory efficiency. Combined with a symmetrized loss function, this framework achieves results of a quality on par with state-of-the-art cryo-EM solvers for both simulated and experimental data, one order of magnitude faster for large datasets and with significantly lower memory requirements than existing methods.

Machine learning has become omnipresent with applications in various safety-critical domains such as medical, law, and transportation. In these domains, high-stake decisions provided by machine learning necessitate researchers to design interpretable models, where the prediction is understandable to a human. In interpretable machine learning, rule-based classifiers are particularly effective in representing the decision boundary through a set of rules comprising input features. Examples of such classifiers include decision trees, decision lists, and decision sets. The interpretability of rule-based classifiers is in general related to the size of the rules, where smaller rules are considered more interpretable. To learn such a classifier, the brute-force direct approach is to consider an optimization problem that tries to learn the smallest classification rule that has close to maximum accuracy. This optimization problem is computationally intractable due to its combinatorial nature and thus, the problem is not scalable in large datasets. To this end, in this paper we study the triangular relationship among the accuracy, interpretability, and scalability of learning rule-based classifiers. The contribution of this paper is an interpretable learning framework IMLI, that is based on maximum satisfiability (MaxSAT) for synthesizing classification rules expressible in proposition logic. IMLI considers a joint objective function to optimize the accuracy and the interpretability of classification rules and learns an optimal rule by solving an appropriately designed MaxSAT query. Despite the progress of MaxSAT solving in the last decade, the straightforward MaxSAT-based solution cannot scale to practical classification datasets containing thousands to millions of samples. Therefore, we incorporate an efficient incremental learning technique inside the MaxSAT formulation by integrating mini-batch learning and iterative rule-learning. The resulting framework learns a classifier by iteratively covering the training data, wherein in each iteration, it solves a sequence of smaller MaxSAT queries corresponding to each mini-batch. In our experiments, IMLI achieves the best balance among prediction accuracy, interpretability, and scalability. For instance, IMLI attains a competitive prediction accuracy and interpretability w.r.t. existing interpretable classifiers and demonstrates impressive scalability on large datasets where both interpretable and non-interpretable classifiers fail. As an application, we deploy IMLI in learning popular interpretable classifiers such as decision lists and decision sets. The source code is available at https://github.com/meelgroup/mlic.