Related papers: Averaging orthogonal projectors
Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local…
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Distributed averaging, or distributed average consensus, is a common method for computing the sample mean of the data dispersed among the nodes of a network in a decentralized manner. By iteratively exchanging messages with neighbors, the…
The issues of bias-correction and robustness are crucial in the strategy of divide-and-conquer (DC), especially for asymmetric nonparametric models with massive data. It is known that quantile-based methods can achieve the robustness, but…
In this paper we propose a special type of aggregation function which generalizes the notion of Ordered Weighted Averaging Function - OWA. The resulting functions are called Dynamic Ordered Weighted Averaging Functions --- DYOWAs. This…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
The rise of internet has resulted in an explosion of data consisting of millions of articles, images, songs, and videos. Most of this data is high dimensional and sparse. The need to perform an efficient search for similar objects in such…
This paper introduces the Class-wise Principal Component Analysis, a supervised feature extraction method for hyperspectral data. Hyperspectral Imaging (HSI) has appeared in various fields in recent years, including Remote Sensing.…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…
Communication is one of the key bottlenecks in the distributed training of large-scale machine learning models, and lossy compression of exchanged information, such as stochastic gradients or models, is one of the most effective instruments…
Transformer architecture has gained popularity due to its ability to scale with large dataset. Consequently, there is a need to reduce the model size and latency, especially for on-device deployment. We focus on vision transformer proposed…
When estimating the treatment effect in an observational study, we use a semiparametric locally efficient dimension reduction approach to assess both the treatment assignment mechanism and the average responses in both treated and…
We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…