Related papers: Less is More: Nystr\"om Computational Regularizati…
Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Conventional stochastic rounding (CSR) is widely employed in the training of neural networks (NNs), showing promising training results even in low-precision computations. We introduce an improved stochastic rounding method, that is simple…
Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the…
The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
We combine K-means clustering with the least-squares kernel classification method. K-means clustering is used to extract a set of representative vectors for each class. The least-squares kernel method uses these representative vectors as a…
Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…
Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…
Neural networks are more expressive when they have multiple layers. In turn, conventional training methods are only successful if the depth does not lead to numerical issues such as exploding or vanishing gradients, which occur less…
We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
In this paper, we study the asymptotic properties of regularized least squares with indefinite kernels in reproducing kernel Krein spaces (RKKS). By introducing a bounded hyper-sphere constraint to such non-convex regularized risk…