arXiv subjects

Lifeng Lai

Publications and source records attributed to Lifeng Lai.

At least 55 records · Page 3Linked to original sources

arXiv2019

Analysis of KNN Information Estimators for Smooth Distributions

KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away from zero in its support. In practice, however, KSG estimator also performs well for a much broader class of distributions, including not only those with bounded support and densities bounded away from zero, but also those with bounded support but densities approaching zero, and those with unbounded support. In this paper, we analyze the convergence rate of the error of KSG estimator for smooth distributions, whose support of density can be both bounded and unbounded. As KSG mutual information estimator can be viewed as an adaptive recombination of KL entropy estimators, in our analysis, we also provide convergence analysis of KL entropy estimator for a broad class of distributions.

stat.ML↗

arXiv2019

Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regression

k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has bounded support and the probability density function is bounded away from zero in its support, the convergence rate of the standard kNN method, in which k is the same for all test samples, is minimax optimal. On the contrary, if the distribution has unbounded support, we show that there is a gap between the convergence rate achieved by the standard kNN method and the minimax bound. To close this gap, we propose an adaptive kNN method, in which different k is selected for different samples. Our selection rule does not require precise knowledge of the underlying distribution of features. The new proposed method significantly outperforms the standard one. We characterize the convergence rate of the proposed adaptive method, and show that it matches the minimax lower bound.

math.ST↗

arXiv2019

On the Adversarial Robustness of Subspace Learning

In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense noises, we consider a more powerful adversary who can first observe the data matrix and then intentionally modify the whole data matrix. We first characterize the optimal rank-one attack strategy that maximizes the subspace distance between the subspace learned from the original data matrix and that learned from the modified data matrix. We then generalize the study to the scenario without the rank constraint and characterize the corresponding optimal attack strategy. Our analysis shows that the optimal strategies depend on the singular values of the original data matrix and the adversary's energy budget. Finally, we provide numerical experiments and practical applications to demonstrate the efficiency of the attack strategies.

eess.SP↗

arXiv2019

On the Adversarial Robustness of Multivariate Robust Estimation

In this paper, we investigate the adversarial robustness of multivariate $M$-Estimators. In the considered model, after observing the whole dataset, an adversary can modify all data points with the goal of maximizing inference errors. We use adversarial influence function (AIF) to measure the asymptotic rate at which the adversary can change the inference result. We first characterize the adversary's optimal modification strategy and its corresponding AIF. From the defender's perspective, we would like to design an estimator that has a small AIF. For the case of joint location and scale estimation problem, we characterize the optimal $M$-estimator that has the smallest AIF. We further identify a tradeoff between robustness against adversarial modifications and robustness against outliers, and derive the optimal $M$-estimator that achieves the best tradeoff.

stat.ML↗

arXiv2019

Towards Ultra-Reliable Low-Latency Communications: Typical Scenarios, Possible Solutions, and Open Issues

Ultra-reliable low-latency communications (URLLC) has been considered as one of the three new application scenarios in the \emph{5th Generation} (5G) \emph {New Radio} (NR), where the physical layer design aspects have been specified. With the 5G NR, we can guarantee the reliability and latency in radio access networks. However, for communication scenarios where the transmission involves both radio access and wide area core networks, the delay in radio access networks only contributes to part of the \emph{end-to-end} (E2E) delay. In this paper, we outline the delay components and packet loss probabilities in typical communication scenarios of URLLC, and formulate the constraints on E2E delay and overall packet loss probability. Then, we summarize possible solutions in the physical layer, the link layer, the network layer, and the cross-layer design, respectively. Finally, we discuss the open issues in prediction and communication co-design for URLLC in wide area large scale networks.

eess.SP↗

arXiv2018

How did Donald Trump Surprisingly Win the 2016 United States Presidential Election? an Information-Theoretic Perspective (Clean Sensing for Big Data Analytics:Optimal Strategies,Estimation Error Bounds Tighter than the Cramér-Rao Bound)

Donald Trump was lagging behind in nearly all opinion polls leading up to the 2016 US presidential election, but he surprisingly won the election. This raises the following important questions: 1) why most opinion polls were not accurate in 2016? and 2) how to improve the accuracies of opinion polls? In this paper, we study the inaccuracies of opinion polls in the 2016 election through the lens of information theory. We first propose a general framework of parameter estimation, called clean sensing (polling), which performs optimal parameter estimation with sensing cost constraints, from heterogeneous and potentially distorted data sources. We then cast the opinion polling as a problem of parameter estimation from potentially distorted heterogeneous data sources, and derive the optimal polling strategy using heterogenous and possibly distorted data under cost constraints. Our results show that a larger number of data samples do not necessarily lead to better polling accuracy, which give a possible explanation of the inaccuracies of opinion polls in 2016. The optimal sensing strategy should instead optimally allocate sensing resources over heterogenous data sources according to several factors including data quality, and, moreover, for a particular data source, it should strike an optimal balance between the quality of data samples, and the quantity of data samples. As a byproduct of this research, in a general setting, we derive a group of new lower bounds on the mean-squared errors of general unbiased and biased parameter estimators. These new lower bounds can be tighter than the classical Cramér-Rao bound (CRB) and Chapman-Robbins bound. Our derivations are via studying the Lagrange dual problems of certain convex programs. The classical Cramér-Rao bound and Chapman-Robbins bound follow naturally from our results for special cases of these convex programs.

cs.IT↗

arXiv2018

Quick Best Action Identification in Linear Bandit Problems

In this paper, we consider a best action identification problem in the stochastic linear bandit setup with a fixed confident constraint. In the considered best action identification problem, instead of minimizing the accumulative regret as done in existing works, the learner aims to obtain an accurate estimate of the underlying parameter based on his action and reward sequences. To improve the estimation efficiency, the learner is allowed to select his action based his historical information; hence the whole procedure is designed in a sequential adaptive manner. We first show that the existing algorithms designed to minimize the accumulative regret is not a consistent estimator and hence is not a good policy for our problem. We then characterize a lower bound on the estimation error for any policy. We further design a simple policy and show that the estimation error of the designed policy achieves the same scaling order as that of the derived lower bound.

cs.LG↗

arXiv2017

Degraded Broadcast Channel with Secrecy Outside a Bounded Range

The $K$-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends $K$ messages to $K$ receivers, and the channel quality gradually degrades from receiver $K$ to receiver 1. Each receiver $k$ is required to decode message $W_1,\ldots,W_k$, for $1\leq k\leq K$, and to be kept ignorant of $W_{k+2},\ldots,W_K$, for $k=1,\ldots, K-2$. Thus, each message $W_k$ is kept secure from receivers with at least two-level worse channel quality, i.e., receivers 1, $\ldots$, $k-2$. The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with binning employed for each layer. Joint embedded coding and binning are employed to protect all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination of $2K$ variables from the order of $K^2$ bounds to obtain a close-form achievable rate region. An outer bound is developed that matches the achievable rate region, whose proof involves recursive construction of the rate bounds and exploits the intuition gained from the achievable scheme.

cs.IT↗

arXiv2017

Efficient Byzantine Sequential Change Detection

In the multisensor sequential change detection problem, a disruption occurs in an environment monitored by multiple sensors. This disruption induces a change in the observations of an unknown subset of sensors. In the Byzantine version of this problem, which is the focus of this work, it is further assumed that the postulated change-point model may be misspecified for an unknown subset of sensors. The problem then is to detect the change quickly and reliably, for any possible subset of affected sensors, even if the misspecified sensors are controlled by an adversary. Given a user-specified upper bound on the number of compromised sensors, we propose and study three families of sequential change-detection rules for this problem. These are designed and evaluated under a generalization of Lorden's criterion, where conditional expected detection delay and expected time to false alarm are both computed in the worst-case scenario for the compromised sensors. The first-order asymptotic performance of these procedures is characterized as the worst-case false alarm rate goes to 0. The insights from these theoretical results are corroborated by a simulation study.

math.ST↗

arXiv2017

Multi-Chart Detection Procedure for Bayesian Quickest Change-Point Detection with Unknown Post-Change Parameters

In this paper, the problem of quickly detecting an abrupt change on a stochastic process under Bayesian framework is considered. Different from the classic Bayesian quickest change-point detection problem, this paper considers the case where there is uncertainty about the post-change distribution. Specifically, the observer only knows that the post-change distribution belongs to a parametric distribution family but he does not know the true value of the post-change parameter. In this scenario, we propose two multi-chart detection procedures, termed as M-SR procedure and modified M-SR procedure respectively, and show that these two procedures are asymptotically optimal when the post-change parameter belongs to a finite set and are asymptotically $ε-$optimal when the post-change parameter belongs to a compact set with finite measure. Both algorithms can be calculated efficiently as their detection statistics can be updated recursively. We then extend the study to consider the multi-source monitoring problem with unknown post-change parameters. When those monitored sources are mutually independent, we propose a window-based modified M-SR detection procedure and show that the proposed detection method is first-order asymptotically optimal when post-change parameters belong to finite sets. We show that both computation and space complexities of the proposed algorithm increase only linearly with respect to the number of sources.

cs.IT↗

arXiv2017

On Randomized Distributed Coordinate Descent with Quantized Updates

In this paper, we study the randomized distributed coordinate descent algorithm with quantized updates. In the literature, the iteration complexity of the randomized distributed coordinate descent algorithm has been characterized under the assumption that machines can exchange updates with an infinite precision. We consider a practical scenario in which the messages exchange occurs over channels with finite capacity, and hence the updates have to be quantized. We derive sufficient conditions on the quantization error such that the algorithm with quantized update still converge. We further verify our theoretical results by running an experiment, where we apply the algorithm with quantized updates to solve a linear regression problem.

stat.ML↗

arXiv2015

Are Slepian-Wolf Rates Necessary for Distributed Parameter Estimation?

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator (MVUE) that has the same performance as that of the optimal estimator in the centralized case while requiring information rates less than the conditions required in the Slepian-Wolf rate region.

cs.IT↗

arXiv2015

Precise Phase Transition of Total Variation Minimization

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.

cs.IT↗

arXiv2014

Byzantine Fault Tolerant Distributed Quickest Change Detection

We introduce and solve the problem of Byzantine fault tolerant distributed quickest change detection in both continuous and discrete time setups. In this problem, multiple sensors sequentially observe random signals from the environment and send their observations to a control center that will determine whether there is a change in the statistical behavior of the observations. We assume that the signals are independent and identically distributed across sensors. An unknown subset of sensors are compromised and will send arbitrarily modified and even artificially generated signals to the control center. It is shown that the performance of the the so-called CUSUM statistic, which is optimal when all sensors are honest, will be significantly degraded in the presence of even a single dishonest sensor. In particular, instead of in a logarithmically the detection delay grows linearly with the average run length (ARL) to false alarm. To mitigate such a performance degradation, we propose a fully distributed low complexity detection scheme. We show that the proposed scheme can recover the log scaling. We also propose a centralized group-wise scheme that can further reduce the detection delay.

math.PR↗

arXiv2014

On the Simulatability Condition in Key Generation Over a Non-authenticated Public Channel

Simulatability condition is a fundamental concept in studying key generation over a non-authenticated public channel, in which Eve is active and can intercept, modify and falsify messages exchanged over the non-authenticated public channel. Using this condition, Maurer and Wolf showed a remarkable "all or nothing" result: if the simulatability condition does not hold, the key capacity over the non-authenticated public channel will be the same as that of the case with a passive Eve, while the key capacity over the non-authenticated channel will be zero if the simulatability condition holds. However, two questions remain open so far: 1) For a given joint probability mass function (PMF), are there efficient algorithms (polynomial complexity algorithms) for checking whether the simulatability condition holds or not?; and 2) If the simulatability condition holds, are there efficient algorithms for finding the corresponding attack strategy? In this paper, we answer these two open questions affirmatively. In particular, for a given joint PMF, we construct a linear programming (LP) problem and show that the simulatability condition holds \textit{if and only if} the optimal value obtained from the constructed LP is zero. Furthermore, we construct another LP and show that the minimizer of the newly constructed LP is a valid attack strategy. Both LPs can be solved with a polynomial complexity.

cs.CR↗

arXiv2014

Bayesian Quickest Change Point Detection with Sampling Right Constraints

In this paper, Bayesian quickest change detection problems with sampling right constraints are considered. Specifically, there is a sequence of random variables whose probability density function will change at an unknown time. The goal is to detect this change in a way such that a linear combination of the average detection delay and the false alarm probability is minimized. Two types of sampling right constrains are discussed. The first one is a limited sampling right constraint, in which the observer can take at most $N$ observations from this random sequence. Under this setup, we show that the cost function can be written as a set of iterative functions, which can be solved by Markov optimal stopping theory. The optimal stopping rule is shown to be a threshold rule. An asymptotic upper bound of the average detection delay is developed as the false alarm probability goes to zero. This upper bound indicates that the performance of the limited sampling right problem is close to that of the classic Bayesian quickest detection for several scenarios of practical interest. The second constraint discussed in this paper is a stochastic sampling right constraint, in which sampling rights are consumed by taking observations and are replenished randomly. The observer cannot take observations if there are no sampling rights left. We characterize the optimal solution, which has a very complex structure. For practical applications, we propose a low complexity algorithm, in which the sampling rule is to take observations as long as the observer has sampling rights left and the detection scheme is a threshold rule. We show that this low complexity scheme is first order asymptotically optimal as the false alarm probability goes to zero.

cs.IT↗

arXiv2014

The Capacity Region of the Source-Type Model for Secret Key and Private Key Generation

The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated, in which each terminal observes a component of correlated sources. All three terminals are required to generate a common secret key concealed from an eavesdropper that has access to public discussion, while two designated terminals are required to generate an extra private key concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established in [1], and was shown to be achievable for one case. In this paper, achievable schemes are designed to achieve the outer bound for the remaining two cases, and hence the SK-PK capacity region is established in general. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound.

cs.IT↗

arXiv2014

An Information Theoretic Approach to Secret Sharing

A novel information theoretic approach is proposed to solve the secret sharing problem, in which a dealer distributes one or multiple secrets among a set of participants that for each secret only qualified sets of users can recover it by pooling their shares together while non-qualified sets of users obtain no information about the secret even if they pool their shares together. While existing secret sharing systems (implicitly) assume that communications between the dealer and participants are noiseless, this paper takes a more practical assumption that the dealer delivers shares to the participants via a noisy broadcast channel. An information theoretic approach is proposed, which exploits the channel as additional resources to achieve secret sharing requirements. In this way, secret sharing problems can be reformulated as equivalent secure communication problems via wiretap channels, and can be solved by employing powerful information theoretic security techniques. This approach is first developed for the classic secret sharing problem, in which only one secret is to be shared. This classic problem is shown to be equivalent to a communication problem over a compound wiretap channel. The lower and upper bounds on the secrecy capacity of the compound channel provide the corresponding bounds on the secret sharing rate. The power of the approach is further demonstrated by a more general layered multi-secret sharing problem, which is shown to be equivalent to the degraded broadcast multiple-input multiple-output (MIMO) channel with layered decoding and secrecy constraints. The secrecy capacity region for the degraded MIMO broadcast channel is characterized, which provides the secret sharing capacity region. Furthermore, these secure encoding schemes that achieve the secrecy capacity region provide an information theoretic scheme for sharing the secrets.

cs.IT↗