A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This work uses tropical geometry to understand neural network decision boundaries.
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…
A set of introductory notes on the subject of data classification using a linear classifier and least-squares cost function, and the negative effect of the presence of outliers on the decision boundary of the linear discriminant. We also show how a simple scaling could make the outlier less significant, thereby obtaini…
Deep neural networks are vulnerable to adversarial attacks and hard to interpret because of their black-box nature. The recently proposed invertible network is able to accurately reconstruct the inputs to a layer from its outputs, thus has the potential to unravel the black-box model. An invertible network classifier c…
Proposes a method to speed up model selection for classification.
Convex polytope trees expand decision trees with interpretable boundaries.
Mixup reduces the sample complexity of finding optimal decision boundaries for more separable data.
The rise in machine learning-assisted decision-making has led to concerns about the fairness of the decisions and techniques to mitigate problems of discrimination. If a negative decision is made about an individual (denying a loan, rejecting an application for housing, and so on) justice dictates that we be able to as…
Enhanced ODT with Feature Concatenation boosts learning efficiency.
We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the ball for and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decisio…
The paper proposes a policy learning framework for interpretable personalization.
The paper explores the geometry and topology of DNN decision boundaries.
This work connects the Hessian to the decision boundary complexity in neural networks.
Many recent works on knowledge distillation have provided ways to transfer the knowledge of a trained network for improving the learning process of a new one, but finding a good technique for knowledge distillation is still an open problem. In this paper, we provide a new perspective based on a decision boundary, which…
Local decision boundary approximation improves model explanations for complex models.
New method initializes sigmoidal MLPs for interpretable shapes.
Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision boundaries, and therefore, many of the studies about deep learning models speculate…
Study decision boundaries using heat diffusion and probabilistic techniques.
In this paper we propose a method to obtain global explanations for trained black-box classifiers by sampling their decision function to learn alternative interpretable models. The envisaged approach provides a unified solution to approximate non-linear decision boundaries with simpler classifiers while retaining the o…
Deep neural networks and in particular, deep neural classifiers have become an integral part of many modern applications. Despite their practical success, we still have limited knowledge of how they work and the demand for such an understanding is evergrowing. In this regard, one crucial aspect of deep neural network c…
Proposes a method to reveal nonlinearities in tensor data.
New method measures generalizability of deep neural networks based on decision boundary complexity.
The paper shows how neural networks with less decision boundary variability generalize better.
Measures neural network decision boundary volume to predict model performance.
Deep learning models generalize by extending decision boundaries outside the convex hull of training data.
FoLDTree improves oblique decision trees with ULDA, enhancing accuracy and feature selection.
While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are often followed by new attacks to defeat them. In this paper, we propose attack-…
New method visualizes decision boundaries of classification models.
Batch normalization improves deep networks by aligning their decision boundaries with data.
We propose the labeled Čech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary fr…
Despite achieving remarkable performance on many image classification tasks, state-of-the-art machine learning (ML) classifiers remain vulnerable to small input perturbations. Especially, the existence of adversarial examples raises concerns about the deployment of ML models in safety- and security-critical environment…
The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical investigation, we show that state-of-t…
A deep neural network (DNN) with piecewise linear activations can partition the input space into numerous small linear regions, where different linear functions are fitted. It is believed that the number of these regions represents the expressivity of the DNN. This paper provides a novel and meticulous perspective to l…
Important insights towards the explainability of neural networks reside in the characteristics of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness, and propose a new perspective that relates dataset features to the distance of samples to the decision boundary. This enabl…
ELECTRE Tree infers ELECTRE Tri-B parameters using a machine learning approach.
Deep neural networks have been widely deployed in various machine learning tasks. However, recent works have demonstrated that they are vulnerable to adversarial examples: carefully crafted small perturbations to cause misclassification by the network. In this work, we propose a novel defense mechanism called Boundary …
We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension. Our technique consists of partitioning the space into simplices and then embedding the data points into features corresponding to the simplices' barycentric coordinates. We then …
Paper proposes a new classifier for hyperbolic spaces using horospherical boundaries.
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…
Extends expected value framework for cost-sensitive causal decision-making.
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or quadratic payoff functions to evaluate their strategies. We find that the fluctuatio…
Develops MGQDA for multi-group classification with theoretical guarantees and practical applications.
Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separab…
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…
Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this behavior by considering the alignment between input image and saliency map. We h…
In this work, we addressed the issue of combining linear classifiers using their score functions. The value of the scoring function depends on the distance from the decision boundary. Two score functions have been tested and four different combination strategies were investigated. During the experimental study, the pro…
EFDA extends LDA to non-Gaussian models using exponential families.
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …