Related papers: How Many Samples Required in Big Data Collection: …
Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process…
Message importance measure (MIM) is an important index to describe the message importance in the scenario of big data. Similar to the Shannon Entropy and Renyi Entropy, MIM is required to characterize the uncertainty of a random process and…
Message importance measure (MIM) is applicable to characterize the importance of information in the scenario of big data, similar to entropy in information theory. In fact, MIM with a variable parameter can make an effect on the…
Information transfer which reveals the state variation of variables usually plays a vital role in big data analytics and processing. In fact, the measures for information transfer could reflect the system change by use of the variable…
Storage and transmission in big data are discussed in this paper, where message importance is taken into account. Similar to Shannon Entropy and Renyi Entropy, we define non-parametric message important measure (NMIM) as a measure for the…
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…
Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure $\nu$ using a random sample of size $n$ drawn from a different probability measure $\mu$. If the two measures $\mu$…
Differential privacy is a leading protection setting, focused by design on individual privacy. Many applications, in medical / pharmaceutical domains or social networks, rather posit privacy at a group level, a setting we call integral…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Rare events attract more attention and interests in many scenarios of big data such as anomaly detection and security systems. To characterize the rare events importance from probabilistic perspective, the message importance measure (MIM)…
Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance sampling-based…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
Adequate sampling is essential for the well-functioning of a market surveillance system. As small as possible statistically significant sample size is the main factor that determines the costs of market surveillance actions. This paper…