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Customer churn describes terminating a relationship with a business or reducing customer engagement over a specific period. Customer acquisition cost can be five to six times that of customer retention, hence investing in customers with…
In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest…
The reversal curse--a language model's inability to infer an unseen fact "B is A" from a learned fact "A is B"--is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode…
Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns…
We consider an \eps-approximation by n-term partial sums of the Karhunen-Lo\`eve expansion to d-parametric random fields of tensor product-type in the average case setting. We investigate the behavior, as d tends to infinity, of the…
The pattern avoidance problem seeks to construct a set $X\subset \mathbb{R}^d$ with large dimension that avoids a prescribed pattern. Examples of such patterns include three-term arithmetic progressions (solutions to $x_1 - 2x_2 + x_3 =…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…
In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…
We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…