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The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
Models based on Convolutional Neural Networks (CNNs) have been proven very successful for semantic segmentation and object parsing that yield hierarchies of features. Our key insight is to build convolutional networks that take input of…
A key problem in automatic analysis and understanding of scientific papers is to extract semantic information from non-textual paper components like figures, diagrams, tables, etc. Much of this work requires a very first preprocessing step:…
Mean field control (MFC) problems have vast applications in artificial intelligence, engineering, and economics, while solving MFC problems accurately and efficiently in high-dimensional spaces remains challenging. This work introduces…
The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…
We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the…
In the current work, a problem-splitting approach and a scheme motivated by transfer learning is applied to a structural health monitoring problem. The specific problem in this case is that of localising damage on an aircraft wing. The…
Convolution neural networks (CNNs) have succeeded in compressive image sensing. However, due to the inductive bias of locality and weight sharing, the convolution operations demonstrate the intrinsic limitations in modeling the long-range…
We consider generating post-hoc explanations of clusters generated from various datasets using auxiliary information which was not used by clustering algorithms. Following terminology used in previous work, we refer to the auxiliary…
This paper aims to define, quantify, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method disentangles feature…
Linguistic features have shown promising applications for detecting various cognitive impairments. To improve detection accuracies, increasing the amount of data or the number of linguistic features have been two applicable approaches.…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…
Computed tomography (CT) imaging could be very practical for diagnosing various diseases. However, the nature of the CT images is even more diverse since the resolution and number of the slices of a CT scan are determined by the machine and…
Learning multiscale Transformer models has been evidenced as a viable approach to augmenting machine translation systems. Prior research has primarily focused on treating subwords as basic units in developing such systems. However, the…
Symmetry in finite model finding problems of many-sorted first-order logic (MSFOL) can be exploited to reduce the number of interpretations considered during search, thereby improving solver performance. In this thesis, we situate symmetry…
This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is…