Related papers: Quantifying the Conceptual Error in Dimensionality…

This paper discusses lexicon word learning in high-dimensional meaning spaces from the viewpoint of referential uncertainty. We investigate various state-of-the-art Machine Learning algorithms and discuss the impact of scaling,…

Machine learning algorithms using deep architectures have been able to implement increasingly powerful and successful models. However, they also become increasingly more complex, more difficult to comprehend and easier to fool. So far, most…

Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a…

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…

Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…

This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an…

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging…

Deep learning models often require large amounts of data for training, leading to increased costs. It is particularly challenging in medical imaging, i.e., gathering distributed data for centralized training, and meanwhile, obtaining…

Symmetry-aware methods for machine learning, such as data augmentation and equivariant architectures, encourage correct model behavior on all transformations (e.g. rotations or permutations) of the original dataset. These methods can…

Missing values, widely called as \textit{sparsity} in literature, is a common characteristic of many real-world datasets. Many imputation methods have been proposed to address this problem of data incompleteness or sparsity. However, the…

Data Cleaning refers to the process of detecting and fixing errors in the data. Human involvement is instrumental at several stages of this process, e.g., to identify and repair errors, to validate computed repairs, etc. There is currently…

Researchers have been facing a difficult problem that data generation mechanisms could be influenced by internal or external factors leading to the training and test data with quite different distributions, consequently traditional…

In this paper, we evaluate dimensionality reduction methods in terms of difficulty in estimating visual information on original images from dimensionally reduced ones. Recently, dimensionality reduction has been receiving attention as the…

The performance of machine learning models relies heavily on the quality of input data, yet real-world applications often face significant data-related challenges. A common issue arises when curating training data or deploying models: two…

When faced with a mathematical model, often the first step is to reduce the complexity of the model by turning variables and parameters into dimensionless quantities. This process is often performed by hand, relying on a skill practiced…

Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or…

The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. Many unsupervised…

To make sense of the world our brains must analyze high-dimensional datasets streamed by our sensory organs. Because such analysis begins with dimensionality reduction, modelling early sensory processing requires biologically plausible…

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider…