Related papers: $L_0$ Isotonic Regression With Secondary Objective…

Isotonic regression is a shape-constrained nonparametric regression in which the regression is an increasing step function. For $n$ data points, the number of steps in the isotonic regression may be as large as $n$. As a result, standard…

The monotonic ordinal classification has increased the interest of researchers and practitioners within machine learning community in the last years. In real applications, the problems with monotonicity constraints are very frequent. To…

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…

Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\'e…

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…

The real-world data is often susceptible to label noise, which might constrict the effectiveness of the existing state of the art algorithms for ordinal regression. Existing works on ordinal regression do not take label noise into account.…

Learning Mahalanobis metric spaces is an important problem that has found numerous applications. Several algorithms have been designed for this problem, including Information Theoretic Metric Learning (ITML) [Davis et al. 2007] and Large…

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal…

We study the sequential calibration of estimations in a quantized isotonic L2 regression setting. We start by showing that the optimal calibrated quantized estimations can be acquired from the traditional isotonic L2 regression solution. We…

Significant advances in flow algorithms have changed the relative performance of various approaches to algorithms for $L_p$ isotonic regression. We show a simple plug-in method to systematically incorporate such advances, and advances in…

Is it possible to perform linear regression on datasets whose labels are shuffled with respect to the inputs? We explore this question by proposing several estimators that recover the weights of a noisy linear model from labels that are…

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physical inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the…

In minimum-cost inverse optimization problems, we are given a feasible solution to an underlying optimization problem together with a linear cost function, and the goal is to modify the costs by a small deviation vector so that the input…

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric…

We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…

In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on…

In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is…

We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total…

Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…

Given a real-valued weighted function $f$ on a finite dag, the $L_p$ isotonic regression of $f$, $p \in [0,\infty]$, is unique except when $p \in [0,1] \cup \{\infty\}$. We are interested in determining a ``best'' isotonic regression for $p…