Efficient Failure Pattern Identification of Predictive Algorithms

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.Comment: 19 pages, Accepted for UAI202

Learning, Large Scale Inference, and Temporal Modeling of Determinantal Point Processes

Determinantal Point Processes (DPPs) are random point processes well-suited for modelling repulsion. In discrete settings, DPPs are a natural model for subset selection problems where diversity is desired. For example, they can be used to select relevant but diverse sets of text or image search results. Among many remarkable properties, they offer tractable algorithms for exact inference, including computing marginals, computing certain conditional probabilities, and sampling. In this thesis, we provide four main contributions that enable DPPs to be used in more general settings. First, we develop algorithms to sample from approximate discrete DPPs in settings where we need to select a diverse subset from a large amount of items. Second, we extend this idea to continuous spaces where we develop approximate algorithms to sample from continuous DPPs, yielding a method to select point configurations that tend to be overly-dispersed. Our third contribution is in developing robust algorithms to learn the parameters of the DPP kernels, which is previously thought to be a difficult, open problem. Finally, we develop a temporal extension for discrete DPPs, where we model sequences of subsets that are not only marginally diverse but also diverse across time

MIMN-DPP: Maximum-information and minimum-noise determinantal point processes for unsupervised hyperspectral band selection

Band selection plays an important role in hyperspectral imaging for reducing the data and improving the efficiency of data acquisition and analysis whilst significantly lowering the cost of the imaging system. Without the category labels, it is challenging to select an effective and low-redundancy band subset. In this paper, a new unsupervised band selection algorithm is proposed based on a new band search criterion and an improved Determinantal Point Processes (DPP). First, to preserve the original information of hyperspectral image, a novel band search criterion is designed for searching the bands with high information entropy and low noise. Unfortunately, finding the optimal solution based on the search criteria to select a low-redundancy band subset is a NP-hard problem. To solve this problem, we consider the correlation of bands from both original hyperspectral image and its spatial information to construct a double-graph model to describe the relationship between spectral bands. Besides, an improved DPP algorithm is proposed for the approximate search of a low-redundancy band subset from the double-graph model. Experiment results on several well-known datasets show that the proposed optical band selection algorithm achieves better performance than many other state-of-the-art methods

A novel band selection and spatial noise reduction method for hyperspectral image classification.

As an essential reprocessing method, dimensionality reduction (DR) can reduce the data redundancy and improve the performance of hyperspectral image (HSI) classification. A novel unsupervised DR framework with feature interpretability, which integrates both band selection (BS) and spatial noise reduction method, is proposed to extract low-dimensional spectral-spatial features of HSI. We proposed a new Neighboring band Grouping and Normalized Matching Filter (NGNMF) for BS, which can reduce the data dimension whilst preserve the corresponding spectral information. An enhanced 2-D singular spectrum analysis (E2DSSA) method is also proposed to extract the spatial context and structural information from each selected band, aiming to decrease the intra-class variability and reduce the effect of noise in the spatial domain. The support vector machine (SVM) classifier is used to evaluate the effectiveness of the extracted spectral-spatial low-dimensional features. Experimental results on three publicly available HSI datasets have fully demonstrated the efficacy of the proposed NGNMF-E2DSSA method, which has surpassed a number of state-of-the-art DR methods

Random matrices: Universality of local spectral statistics of non-Hermitian matrices

It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process on $\mathbb{C}$ with kernel $K_{\infty}(z,w):=\frac{1}{\pi}e^{-|z|^2/2-|w|^2/2+z\bar{w}}$ in the limit $n\to\infty$. In this paper, we show that this asymptotic law is universal among all random $n\times n$ matrices $M_n$ whose entries are jointly independent, exponentially decaying, have independent real and imaginary parts and whose moments match that of the complex Gaussian ensemble to fourth order. Analogous results at the edge of the spectrum are also obtained. As an application, we extend a central limit theorem for the number of eigenvalues of complex Gaussian matrices in a small disk to these more general ensembles. These results are non-Hermitian analogues of some recent universality results for Hermitian Wigner matrices. However, a key new difficulty arises in the non-Hermitian case, due to the instability of the spectrum for such matrices. To resolve this issue, we the need to work with the log-determinants $\log|\det(M_n-z_0)|$ rather than with the Stieltjes transform $\frac{1}{n}\operatorname {tr}(M_n-z_0)^{-1}$, in order to exploit Girko's Hermitization method. Our main tools are a four moment theorem for these log-determinants, together with a strong concentration result for the log-determinants in the Gaussian case. The latter is established by studying the solutions of a certain nonlinear stochastic difference equation. With some extra consideration, we can extend our arguments to the real case, proving universality for correlation functions of real matrices which match the real Gaussian ensemble to the fourth order. As an application, we show that a real $n\times n$ matrix whose entries are jointly independent, exponentially decaying and whose moments match the real Gaussian ensemble to fourth order has $\sqrt{\frac{2n}{\pi}}+o(\sqrt{n})$ real eigenvalues asymptotically almost surely.Comment: Published in at http://dx.doi.org/10.1214/13-AOP876 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing

This thesis will address the fusion of multiple data sources arising in remote sensing, such as hyperspectral and LIDAR. Fusing of multiple data sources provides better data representation and classification results than any of the independent data sources would alone. We begin our investigation with the well-studied Laplacian Eigenmap (LE) algorithm. This algorithm offers a rich template to which fusion concepts can be added. For each phase of the LE algorithm (graph, operator, and feature space) we develop and test different data fusion techniques. We also investigate how partially labeled data and approximate LE preimages can used to achieve data fusion. Lastly, we study several numerical acceleration techniques that can be used to augment the developed algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nystrom extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nystrom extension