arXiv research

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (i…

ParK efficiently solves kernel ridge regression for large datasets.

Improved supervised EM learning for shared kernel models with feature space partitioning.

GRANITE unifies feature-based explanation methods to reduce disagreement.

Oblique BART improves tree-based predictions.

A post-hoc framework improves model performance by calibrating different feature spaces.

Survey of Bayesian nonparametric space partition models and their applications.

GADGET framework decomposes global feature effects using recursive partitioning.

We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which takes into account natural gaps in the data between clusters. Geometric features …

Backdoor attacks are possible in feature-partitioned collaborative learning, even without labels.

The Maximum Mutual Information (MMI) criterion is different from the Least Error Rate (LER) criterion. It can reduce failing to report small probability events. This paper introduces the Channels Matching (CM) algorithm for the MMI classifications of unseen instances. It also introduces some semantic information method…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each partition set. We propose an alternative approach, which avoids such partitioning and…

With the advent of highly predictive but opaque deep learning models, it has become more important than ever to understand and explain the predictions of such models. Existing approaches define interpretability as the inverse of complexity and achieve interpretability at the cost of accuracy. This introduces a risk of …

Algorithm clusters items by sequentially selecting features, minimizing observations.

We introduce a novel approach to feed-forward neural network interpretation based on partitioning the space of sequences of neuron activations. In line with this approach, we propose a model-specific interpretation method, called YASENN. Our method inherits many advantages of model-agnostic distillation, such as an abi…

Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance. Basically, it integrates multi-view information into graphs, which are then fed into sp…

New estimator for joint entropy outperforms existing methods in various distributions.

RIPE is a novel deterministic and easily understandable prediction algorithm developed for continuous and discrete ordered data. It infers a model, from a sample, to predict and to explain a real variable $Y$ given an input variable $X \in \mathcal X$ (features). The algorithm extracts a sparse set of hyperrectangles $…

FairGP uses graph partitioning to make Graph Transformers fair and scalable.

A new approach uses partial likelihood to improve tree-based density estimation and inference.

The paper examines topological features of ReLU networks and their relation to decision boundaries and training loss.

Develops methods to analyze feature-outcome associations in subpopulations.

Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over those under the setting where data is partitioned on samples, especially when the …

Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…

A method to improve clustering explainability using bagging and feature dropout.

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we…

The study analyzes decision trees on real and categorical features, deriving bounds on their VC dimension and proposing improved pruning algorithms.

FDSKL algorithm trains vertically partitioned data with kernels securely and efficiently.

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a barrier to the adoption of these methods since medical researchers are required to pr…

Proposes a partitioned least squares model for feature grouping.

We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a $p$-dimensional feature space. By conducting the Delaunay triangulation algorithm on the data points, the DTL partitions the feature space into a series of $p$-d…

Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…

Online BSP-Forest improves space partitioning for large-scale classification and regression.

Algorithm improves binary classification of biased grouped data.

MD-split+ creates locally valid prediction regions for complex data.

This paper proposes a method to learn graph representations by partitioning edges into communities.

Imputation-free method learns tabular data with missing values using transformer.

DMFAW improves multi-view clustering with adaptive weights and feature selection.

Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions re…

In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a partition. The estimator predicts the empirical conditional expectation over the cel…

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within a…

In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of $k$ product distributions. We are interested in the case that individual features are of low average quality $γ$, and we want to use as few of them as possible to correctly partition the sample. We analyze a spectral tech…

Survey of mass partition problems in geometry and topology.

Quantized-TinyLLaVA reduces communication costs in split learning for multimodal models.

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as …

Optimizes Lipschitz estimates for partitions of unity and characterizes spaces with Assouad-Nagata dimension.

Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic …

SplitNN-driven Vertical Partitioning enables distributed learning from diverse data sources.