Related papers: Optimal Piecewise Local-Linear Approximations
Recent advancements in Large Language Models (LLMs) have demonstrated exceptional capabilities in complex tasks like machine translation, commonsense reasoning, and language understanding. One of the primary reasons for the adaptability of…
In this paper, we propose symbolic decision trees as surrogate models for approximating model predictive control laws. The proposed approach learns simultaneously the partition of the input domain (splitting logic) as well as local…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
While deep neural networks are extremely effective at classifying images, they remain opaque and hard to interpret. We introduce local and global explanation methods for black-box models that generate explanations in terms of…
Most state-of-the-art machine learning algorithms induce black-box models, preventing their application in many sensitive domains. Hence, many methodologies for explaining machine learning models have been proposed to address this problem.…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…
Complex black-box predictive models may have high performance, but lack of interpretability causes problems like lack of trust, lack of stability, sensitivity to concept drift. On the other hand, achieving satisfactory accuracy of…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
Machine learning models are increasingly used in critical applications but are mostly "black boxes" due to their lack of transparency. Local explanation approaches, such as LIME, address this issue by approximating the behavior of complex…
We consider learning to optimize a classification metric defined by a black-box function of the confusion matrix. Such black-box learning settings are ubiquitous, for example, when the learner only has query access to the metric of…
Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…
With the increasing adoption of predictive models trained using machine learning across a wide range of high-stakes applications, e.g., health care, security, criminal justice, finance, and education, there is a growing need for effective…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…
A main drawback of eXplainable Artificial Intelligence (XAI) approaches is the feature independence assumption, hindering the study of potential variable dependencies. This leads to approximating black box behaviors by analyzing the effects…
We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general…
We present an approach to explain the decisions of black box models for image classification. While using the black box to label images, our explanation method exploits the latent feature space learned through an adversarial autoencoder.…
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical works, a complete understanding is still missing. Apart…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…