اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDiscussion of: Treelets--An adaptive multi-Scale basis for sparse unordered data
11
0
0.0
(
0
)
تأليف
Fionn Murtagh
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Discussion of Treelets--An adaptive multi-Scale basis for sparse unordered data [arXiv:0707.0481]
قيم البحث
اقرأ أيضاً
Forecasting accuracy of mortality data is important for the management of pension funds and pricing of life insurance in actuarial science. Age-specific mortality forecasting in the US poses a challenging problem in high dimensional time series analy
sis. Prior attempts utilize traditional dimension reduction techniques to avoid the curse of dimensionality, and then mortality forecasting is achieved through features forecasting. However, a method of reducing dimension pertinent to ideal forecasting is elusive. To address this, we propose a novel approach to pursue features that are not only capable of representing original data well but also capturing time-serial dependence as most as possible. The proposed method is adaptive for the US mortality data and enjoys good statistical performance. As a comparison, our method performs better than existing approaches, especially in regard to the Lee-Carter Model as a benchmark in mortality analysis. Based on forecasting results, we generate more accurate estimates of future life expectancies and prices of life annuities, which can have great financial impact on life insurers and social securities compared with using Lee-Carter Model. Furthermore, various simulations illustrate scenarios under which our method has advantages, as well as interpretation of the good performance on mortality data.
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of
the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M <= W <= N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signals covariance matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series. A real application is to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 4 and 3 years supports the Devils staircase scenario for the El Nino/Southern Oscillation phenomenon.
We develop a new methodology for spatial regression of aggregated outputs on multi-resolution covariates. Such problems often occur with spatial data, for example in crop yield prediction, where the output is spatially-aggregated over an area and the
covariates may be observed at multiple resolutions. Building upon previous work on aggregated output regression, we propose a regression framework to synthesise the effects of the covariates at different resolutions on the output and provide uncertainty estimation. We show that, for a crop yield prediction problem, our approach is more scalable, via variational inference, than existing multi-resolution regression models. We also show that our framework yields good predictive performance, compared to existing multi-resolution crop yield models, whilst being able to provide estimation of the underlying spatial effects.
This paper proposes a global approach for the multi-view registration of unordered range scans. As the basis of multi-view registration, pair-wise registration is very pivotal. Therefore, we first select a good descriptor and accelerate its correspon
dence propagation for the pair-wise registration. Then, we design an effective rule to judge the reliability of pair-wise registration results. Subsequently, we propose a model augmentation method, which can utilize reliable results of pair-wise registration to augment the model shape. Finally, multi-view registration can be accomplished by operating the pair-wise registration and judgment, and model augmentation alternately. Experimental results on public available data sets show, that this approach can automatically achieve the multi-view registration of unordered range scans with good accuracy and effectiveness.
In the class of streaming anomaly detection algorithms for univariate time series, the size of the sliding window over which various statistics are calculated is an important parameter. To address the anomalous variation in the scale of the pseudo-pe
riodicity of time series, we define a streaming multi-scale anomaly score with a streaming PCA over a multi-scale lag-matrix. We define three methods of aggregation of the multi-scale anomaly scores. We evaluate their performance on Yahoo! and Numenta dataset for unsupervised anomaly detection benchmark. To the best of authors knowledge, this is the first time a multi-scale streaming anomaly detection has been proposed and systematically studied.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
