Related papers: Using Enriched Category Theory to Construct the Ne…

This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…

In machine learning, crowdsourcing is an economical way to label a large amount of data. However, the noise in the produced labels may deteriorate the accuracy of any classification method applied to the labelled data. We propose an…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours…

Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…

The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such…

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb P(Y = m | X = x) = \eta_m(x)$, $1 \leq m \leq M$, and $\eta_1(x), \dots, \eta_M(x)$ are…

Given a training set $P \subset \mathbb{R}^d$, the nearest-neighbor classifier assigns any query point $q \in \mathbb{R}^d$ to the class of its closest point in $P$. To answer these classification queries, some training points are more…

We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary monoidal $\infty$-category $\mathcal{V}$. Our theory of enriched $\infty$-categories has many desirable properties; for instance, if the enriching…

In this paper, a novel K-Nearest Neighbour and Support Vector Machine hybrid classification technique has been proposed that is simple and robust. It is based on the concept of discriminative nearest neighbourhood classification. The…

The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…

We prove that an enriched $\infty$-category is completely determined by its enriched presheaf category together with a `marking' by the representable presheaves. More precisely, for any presentably monoidal $\infty$-category $\mathcal{V}$…

In recent years, many deep-learning based models are proposed for text classification. This kind of models well fits the training set from the statistical point of view. However, it lacks the capacity of utilizing instance-level information…

In humans and other animals, category learning enhances discrimination between stimuli close to the category boundary. This phenomenon, called categorical perception, was also empirically observed in artificial neural networks trained on…

Nearest neighbors (NN) are traditionally used to compute final decisions, e.g., in Support Vector Machines or k-NN classifiers, and to provide users with explanations for the model's decision. In this paper, we show a novel utility of…

Deep neural networks have been the driving force behind the success in classification tasks, e.g., object and audio recognition. Impressive results and generalization have been achieved by a variety of recently proposed architectures, the…

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…

Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown classes. The recently introduced…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…