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Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space
No full text在這篇論文中，我們提出了「稀疏隨機特徵近似—希伯特空間下的座標下降法」(Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space )。這個演算法的大致流程是，首先我們會在希伯特空間上去最小化L1正規化(L1-Regularization)的目標函式(objective)，然後經過數個迴圈的隨機座標下降法(Randomized Coordinate Descent, RCD)訓練(training)，最後會得到一個稀疏非線性的預測器(predictor)。藉由將這個演算法解釋成在無窮維度的隨機特徵座標下降，可以證明我們提出的方法會收斂至一個不差於實際核心解(exact kernel solution)ϵ-準確度(precision)的解，也就是只需抽取O(1/ϵ)數量的隨機特徵，就能將期望上的錯誤率降低到ϵ以下，反而是目前隨機特徵法使用的蒙地卡羅分析法(Monte-Carlo analysis) 卻需要抽取O(1/ϵ^2 )數量的隨機特徵，才能達到相同的正確率。在我們的實驗中，稀疏隨機特徵演算法會得到一個稀疏的解，且在訓練的過程中使用了較少的記憶體(memory) 以及較少的預測(prediction) 時間，且不論是在迴歸(regression)或是分類(classification)的問題上，都同時保持與核心機器(kernel machine)相當的表現(performance)。除此之外，在無窮維度(infinite-dimensional)下的L1正規化問題上，當提升演算法(boosting approach) 無法使用貪婪步驟(greedy step)求得準確的值的時候，我們使用的近似求解器(approximate solver)以及隨機方法(randomized approach)可以得到一個比提升演算法更好的解。In this paper, we propose a Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space, which learns a sparse non-linear predictor by minimizing an ℓ1-regularized objective function over the Hilbert Space induced from kernel function. By interpreting the algorithm as Randomized Coordinate Descent in the infinite-dimensional space, we show the proposed approach converges to a solution comparable within ϵ-precision to exact kernel method by drawing O(1/ϵ) number of random features, contrasted to the O(1/ϵ^2)-type convergence achieved by Monte-Carlo analysis in current Random Feature literature. In our experiments, the Sparse Random Feature algorithm obtains sparse solution that requires less memory and prediction time while maintains comparable performance on tasks of regression and classification. In the meantime, as an approximate solver for infinite-dimensional ℓ1-regularized problem, the randomized approach converges to better solution than Boosting approach when the greedy step of Boosting cannot be performed exactly.致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vii
List of Tables viii
1 Introduction 1
2 Related Work 3
2.1 Kernel Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Low-Rank Approximation . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Random Feature . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Randomized Coordinate Descent . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Why existing RCD analysis cannot be applied in our setting . . . 5
3 Problem Setup 7
3.1 Preliminary Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.1 Representer Theorem . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.2 Kernel Approximation . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.3 Reproducing Kernel Hilbert Space (RKHS) . . . . . . . . . . . . 8
3.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.1 Kernel and Feature Map . . . . . . . . . . . . . . . . . . . . . . 10
3.2.2 Random Feature as Monte-Carlo Approximation . . . . . . . . . 11
4 Theorem and Algorithm 13
4.1 Sparse Random Feature as Coordinate Descent . . . . . . . . . . . . . . 13
4.1.1 Convergence Analysis . . . . . . . . . . . . . . . . . . . . . . . 14
4.1.2 Relation to Kernel Method . . . . . . . . . . . . . . . . . . . . . 19
4.1.3 Relation to Boosting Method . . . . . . . . . . . . . . . . . . . . 20
5 Implementation 21
5.1 Implementation for Random Feature Generator . . . . . . . . . . . . . . 22
5.1.1 Random Fourier Feature . . . . . . . . . . . . . . . . . . . . . . 23
5.1.2 Random Perceptron Feature . . . . . . . . . . . . . . . . . . . . 23
5.2 Implementation for different solvers . . . . . . . . . . . . . . . . . . . . 24
5.2.1 Sparse Random Feature as Coordinate Descent . . . . . . . . . . 24
5.2.2 Random Feature with L2-Regularization setting . . . . . . . . . . 25
5.2.3 Kernel Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 Experiments 26
6.1 Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.3.1 Training Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.3.2 Testing Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.3 Memory Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.4 Testing Performance . . . . . . . . . . . . . . . . . . . . . . . . 29
7 Conclusions 32
7.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
A Proof of Lemma 1 34
B Proof of Corollary 2 35
Bibliography 3
Land Use Suitability Evaluation in Nei Shung Xi Area
No full text本研究主要就土地可開發利用程度做評估判斷。由於土地超限利用會引發災害，甚至可能對人類造成不可逆的傷害，如何防止災害成為研究目標。若能判斷土地乘載量，各土地利用類型皆在限度內使用土地，則可期望災害減到最低。近年來國內外皆有土地評估相關的研究，其中一個方法為適地性評估(land suitability evaluation)，蒐集環境與人為因子，將各因子的圖層套疊，並據此判斷土地使用類別的適宜性，將所得匯整為複合性適宜圖作為開發利用的政策考量。而台灣現下對於土地評估的研究較為稀少且落後，因此本研究大略蒐集國內外相關適地性評估研究，以供日後研究參考。並利用可取得的土地資料，使用U/L ratio 評估法，企圖以簡潔明瞭的方式盡可能的客觀判斷土地可利用程度，期望能有效遏止因超限利用導致的傷害。U/L ratio 評估法是由陳信雄教授提出，將土地條件與使用類型個別設立相對應的評估分數，比值為一表示適地使用。研究結果顯示內雙溪地區的土地開發利用潛力並不高，開發程度因受到管制，為低度開發，較無超限利用的問題。適地性評估需依土地類型不同而設立不同評估條件，本研究以內雙溪地區為研究對象。研究結果顯示，研究區域內土地條件不高，土地利用程度也不高，僅有少數地區超限利用，另外有部分地區具備開發潛力。
評估條件無法直接套用於他類土地，故日後有相關研究仍須依目的，設立評估標準。This study aimed at land suitability evaluation(LSU) to explore the better land use type, and analysing U/L ratio method to show the conclusion. U/L ratio method is raised from pro-fessor Shin-Shun Chen, to set the correspondent grades on land and land use, and ratio=1 mean suitable use. There is lack of research of LSU in Taiwan, so except for the area study, in this literature also collect some research in recent years about LSU. This study area is located in Neishanggsi Forestry Nature Park, the fringe of Taipei
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
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