Feature representation is an important aspect of remote-sensing based image classification. While deep convolutional neural networks are able to effectively amalgamate information, large numbers of parameters often make learned features inscrutable and difficult to transfer to alternative models. In order to better represent statistical texture information for remote-sensing image classification, in this paper, we investigate performing joint dimensionality reduction and classification using a novel histogram neural network. Motivated by a popular dimensionality reduction approach, t-Distributed Stochastic Neighbor Embedding (t-SNE), our proposed method incorporates a classification loss computed on samples in a low-dimensional embedding space. We compare the learned sample embeddings against coordinates found by t-SNE in terms of classification accuracy and qualitative assessment. We also explore use of various divergence measures in the t-SNE objective. The proposed method has several advantages such as readily embedding out-of-sample points and reducing feature dimensionality while retaining class discriminability. Our results show that the proposed approach maintains and/or improves classification performance and reveals characteristics of features produced by neural networks that may be helpful for other applications.
New Jersey Institute of Technology（新泽西理工学院）；Bremen University of Applied Sciences（不来梅应用技术大学）；Princeton University（普林斯顿大学）；Technion - Israel Institute of Technology（以色列理工学院）
A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an exp…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower dimensionality, our approach aims to preserve the nonnegative components of the data that are important for classification. We identify these components from the support vectors of large-margin classifiers and derive iterative updates to preserve them in a semi-supervised version of NMF. These updates have a simple multiplicative form like their unsupervised counter…
Hyperbolic space can naturally embed hierarchies that often exist in real-world data and semantics. While high-dimensional hyperbolic embeddings lead to better representations, most hyperbolic models utilize low-dimensional embeddings, due to non-trivial optimization and visualization of high-dimensional hyperbolic data. We propose CO-SNE, which extends the Euclidean space visualization tool, t-SNE, to hyperbolic space. Like t-SNE, it converts distances between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of high-dimen…
Maximum entropy approach to classification is very well studied in applied statistics and machine learning and almost all the methods that exists in literature are discriminative in nature. In this paper, we introduce a maximum entropy classification method with feature selection for large dimensional data such as text datasets that is generative in nature. To tackle the curse of dimensionality of large data sets, we employ conditional independence assumption (Naive Bayes) and we perform feature selection simultaneously, by enforcing a `maximum discrimination' between estimated class condition…
Johns Hopkins University（约翰斯·霍普金斯大学）；Flatiron Institute（熨斗研究所）；New York University（纽约大学）
Overparameterization in deep learning is powerful: Very large models fit the training data perfectly and yet often generalize well. This realization brought back the study of linear models for regression, including ordinary least squares (OLS), which, like deep learning, shows a "double-descent" behavior: (1) The risk (expected out-of-sample prediction error) can grow arbitrarily when the number of parameters $p$ approaches the number of samples $n$, and (2) the risk decreases with $p$ for $p>n$, sometimes achieving a lower value than the lowest risk for $p<n$. The divergence of the risk for O…
Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；Max Planck Institute for Human Cognitive and Brain Sciences（马克斯·普朗克人类认知与脑科学研究所）；Max Planck School of Cognition（马克斯·普朗克认知学校）；ScaDS.AI (Center for Scalable Data Analytics and AI)（ScaDS.AI（可扩展数据与人工智能中心））；Santa Fe Institute for the Sciences of Complexity（复杂性科学圣菲研究所）
Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reduction
Seoul National University（首尔国立大学）；University of California, Davis（加州大学戴维斯分校）；Qatar Computing Research Institute, Hamad Bin Khalifa University（哈马德·本·哈利法大学卡塔尔计算研究所）
Yale University（耶鲁大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
The wide variety of motions performed by the human arm during daily tasks makes it desirable to find representative subsets to reduce the dimensionality of these movements for a variety of applications, including the design and control of robotic and prosthetic devices. This paper presents a novel method and the results of an extensive human subjects study to obtain representative arm joint angle trajectories that span naturalistic motions during Activities of Daily Living (ADLs). In particular, we seek to identify sets of useful motion trajectories of the upper limb that are functions of a si…
We consider the off-policy evaluation problem of reinforcement learning using deep convolutional neural networks. We analyze the deep fitted Q-evaluation method for estimating the expected cumulative reward of a target policy, when the data are generated from an unknown behavior policy. We show that, by choosing network size appropriately, one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Specifically, we establish a sharp error bound for fitted Q-e…
University of Granada（格拉纳达大学）；University of Jaén（哈恩大学）；King Abdulaziz University（阿卜杜勒阿齐兹国王大学）
Available data in machine learning applications is becoming increasingly complex, due to higher dimensionality and difficult classes. There exists a wide variety of approaches to measuring complexity of labeled data, according to class overlap, separability or boundary shapes, as well as group morphology. Many techniques can transform the data in order to find better features, but few focus on specifically reducing data complexity. Most data transformation methods mainly treat the dimensionality aspect, leaving aside the available information within class labels which can be useful when classe…
Tianjin University（天津大学）；The Open University（开放大学）；The Hong Kong Polytechnic University（香港理工大学）
Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) principle to maximally preserve parameters with confident estimates and rule out unreliable or noisy parameters. Formally, the confidence of a parameter can be assessed by its Fisher information, which establishes a connection with the inverse variance of any unbiased estimate for th…
We propose a Multiscale Invertible Generative Network (MsIGN) and associated training algorithm that leverages multiscale structure to solve high-dimensional Bayesian inference. To address the curse of dimensionality, MsIGN exploits the low-dimensional nature of the posterior, and generates samples from coarse to fine scale (low to high dimension) by iteratively upsampling and refining samples. MsIGN is trained in a multi-stage manner to minimize the Jeffreys divergence, which avoids mode dropping in high-dimensional cases. On two high-dimensional Bayesian inverse problems, we show superior pe…
