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We present a forward sufficient dimension reduction method for categorical or ordinal responses by extending the outer product of gradients and minimum average variance estimator to multinomial generalized linear model. Previous work in…
Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and…
Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
The problem of testing low-degree polynomials has received significant attention over the years due to its importance in theoretical computer science, and in particular in complexity theory. The problem is specified by three parameters:…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
We consider the problem of surrogate sufficient dimension reduction, that is, estimating the central subspace of a regression model, when the covariates are contaminated by measurement error. When no measurement error is present, a…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…
Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
Katz and Sarnak conjectured a correspondence between the $n$-level density statistics of zeros from families of $L$-functions with eigenvalues from random matrix ensembles. In many cases the sums of smooth test functions, whose Fourier…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
A reduced-bias nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved…
In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…
Catastrophic forgetting (CF) occurs when a neural network loses the information previously learned while training on a set of samples from a different distribution, i.e., a new task. Existing approaches have achieved remarkable results in…