Related papers: Building an interpretable fuzzy rule base from dat…
The partial least squares (PLS) is a popular modeling technique commonly used in social sciences. The traditional PLS algorithm deals with variables measured on interval scales while data are often collected on ordinal scales: a…
Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive…
In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the…
The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…
Optical microrobots actuated by optical tweezers (OT) offer great potential for biomedical applications such as cell manipulation and microscale assembly. These tasks demand accurate three-dimensional perception to ensure precise control in…
The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate…
Orthogonal least squares (OLS) is a classic algorithm for sparse recovery, function approximation, and subset selection. In this paper, we analyze the performance guarantee of the OLS algorithm. Specifically, we show that OLS guarantees the…
In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian…
The statistical essence of the Transformer architecture has long remained elusive: Is it a universal approximator, or a neural network version of known computational algorithms? Through rigorous algebraic proof, we show that the latter…
High-dimensional compositional data are commonplace in the modern omics sciences amongst others. Analysis of compositional data requires a proper choice of orthonormal coordinate representation as their relative nature is not compatible…
Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not…
In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…
In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…
There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the…
Ordinal regression bridges regression and classification by assigning objects to ordered classes. While human experts rely on discriminative patch-level features for decisions, current approaches are limited by the availability of only…
Deep learning models are often unaware of the inherent constraints of the task they are applied to. However, many downstream tasks require logical consistency. For ontology classification tasks, such constraints include subsumption and…
Type-1 and Interval Type-2 (IT2) Fuzzy Logic Systems (FLS) excel in handling uncertainty alongside their parsimonious rule-based structure. Yet, in learning large-scale data challenges arise, such as the curse of dimensionality and training…
Real-world data contain uncertainty and variations that can be correlated to external variables, known as randomness. An alternative cause of randomness is chaos, which can be an important component of chaotic time series. One of the…
This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…