arXiv subjects

Thuan Nguyen

Publications and source records attributed to Thuan Nguyen.

24 records · Page 2Linked to original sources

arXiv2020

Communication-Channel Optimized Partition

Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the posterior probability p(X|Y). This result finally provides a polynomial-time algorithm to find the globally optimal quantizer.

cs.IT↗

arXiv2019

Minimizing Impurity Partition Under Constraints

Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there exists a wealth of literature on approximate algorithms and theoretical analyses of the partitioning problem under different settings. In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC). MIPUC finds an optimal partition that minimizes a given loss function under a given concave constraint. MIPUC generalizes the recently proposed deterministic information bottleneck problem which finds an optimal partition that maximizes the mutual information between the input and partition output while minimizing the partition output entropy. Our proposed algorithm is developed based on a novel optimality condition, which allows us to find a locally optimal solution efficiently. Moreover, we show that the optimal partition produces a hard partition that is equivalent to the cuts by hyperplanes in the probability space of the posterior probability that finally yields a polynomial time complexity algorithm to find the globally optimal partition. Both theoretical and numerical results are provided to validate the proposed algorithm.

cs.IT↗

arXiv2017

Inverse of a Special Matrix and Application

The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have shown an inverse closed form for an interesting matrix which has much applications in communication system. Base on this inverse closed form, the channel capacity closed form of a communication system can be determined via the error rate parameter alpha

cs.DM↗

arXiv2017

Achievable Rate Regions Using Novel Location Assisted Coding (LAC)

The recent increase in number of wireless devices has been driven by the growing markets of smart homes and the Internet of Things (IoT). As a result, expanding and/or efficient utilization of the radio frequency (RF) spectrum is critical to accommodate such an increase in wireless bandwidth. Alternatively, recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. Since FSO transmission does not interfere with the RF signals, such a system can be integrated with the current WiFi systems to provide orders of magnitude improvement in bandwidth. A novel component of WiFO is its ability to jointly encode bits from different flows for optimal transmissions. In this paper, we introduce the WiFO architecture and a novel cooperative transmission framework using location assisted coding (LAC) technique to increase the overall wireless capacity. Specifically, achievable rate regions for WiFO using LAC will be characterized. Both numerical and theoretical analyses are given to validate the proposed coding schemes.

cs.IT↗

arXiv2016

A Unified Monte-Carlo Jackknife for Small Area Estimation after Model Selection

We consider estimation of measure of uncertainty in small area estimation (SAE) when a procedure of model selection is involved prior to the estimation. A unified Monte-Carlo jackknife method, called McJack, is proposed for estimating the logarithm of the mean squared prediction error. We prove the second-order unbiasedness of McJack, and demonstrate the performance of McJack in assessing uncertainty in SAE after model selection through empirical investigations that include simulation studies and real-data analyses.

stat.CO↗

arXiv2008

Fence methods for mixed model selection

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.

math.ST↗