Related papers: A new approach to generalisation error of machine …
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
We introduce a new procedure for training of artificial neural networks by using the approximation of an objective function by arithmetic mean of an ensemble of selected randomly generated neural networks, and apply this procedure to the…
This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…
A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…
We propose a novel method for training deep neural networks that are capable of interpolation, that is, driving the empirical loss to zero. At each iteration, our method constructs a stochastic approximation of the learning objective. The…
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…
The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample $x$ whenever this sample falls inside or on the boundary of the given dataset's…
We present a novel class incremental learning approach based on deep neural networks, which continually learns new tasks with limited memory for storing examples in the previous tasks. Our algorithm is based on knowledge distillation and…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
This work presents a supervised learning based approach to the computer vision problem of frame interpolation. The presented technique could also be used in the cartoon animations since drawing each individual frame consumes a noticeable…
Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…
This paper introduces a novel perspective about error in machine learning and proposes inverse feature learning (IFL) as a representation learning approach that learns a set of high-level features based on the representation of error for…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…
Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases,…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
This paper presents an edge-based defocus blur estimation method from a single defocused image. We first distinguish edges that lie at depth discontinuities (called depth edges, for which the blur estimate is ambiguous) from edges that lie…
As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…
In this paper we propose a method of obtaining points of extreme overfitting - parameters of modern neural networks, at which they demonstrate close to 100 % training accuracy, simultaneously with almost zero accuracy on the test sample.…