Talagrand’s inductive method and isoperimetric inequalities involving random sets

The Dirichlet-Ferguson measure is a cornerstone in nonparametric Bayesian statistics and the study of the distributional properties of expectations with respect to such measure is an important line of research initiated in Cifarelli and Regazzini (1979a,b) and still very active, see Letac and Piccioni (2018) and Lijoi and Prnster (2009).In this paper we provide explicit upper bounds for the d 3 , the d 2 and the convex distances between random vectors whose components are means of the Dirichlet-Ferguson measure and a random vector distributed according to the multivariate Gaussian law.These results are applied to the Gaussian approximation of linear transformations of random vectors with the Dirichlet distribution, yielding presumably optimal rates on the d 3 and the d 2 distances and presumably suboptimal rates on the convex and the Kolmogorov distances.

In this paper, we propose a novel broad coverage precoder design for three-dimensional (3D) massive multi-input multi-output (MIMO) equipped with huge uniform planar arrays (UPAs). The desired two-dimensional (2D) angle power spectrum is assumed to be separable. We use the per-antenna constant power constraint and the semi-unitary constraint which are widely used in the literature. For normal broad coverage precoder design, the dimension of the optimization space is the product of the number of antennas at the base station (BS) and the number of transmit streams. With the proposed method, the design of the high-dimensional precoding matrices is reduced to that of a set of low-dimensional orthonormal vectors, and of a pair of low-dimensional vectors. The dimensions of the vectors in the set and the pair are the number of antennas per column and per row of the UPA, respectively. We then use optimization methods to generate the set of orthonormal vectors and the pair of vectors, respectively. Finally, simulation results show that the proposed broad coverage precoding matrices achieve nearly the same performance as the normal broad coverage precoder with much lower computational complexity.

A Monte Carlo method for calculating strength functions in many-fermion systems

We present experimental findings on the decoding failure rate (DFR) of BIKE, a fourth-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level. We select parameters according to BIKE design principles and conduct a series of experiments. We directly compute the average DFR on a range of BIKE block sizes and identify both the waterfall and error floor regions of the DFR curve. We then study the influence on the average DFR of three sets \(\mathcal {C}\), \(\mathcal {N}\), and \(2\mathcal {N}\) of near-codewords—vectors of low weight that induce syndromes of low weight—defined by Vasseur in 2021. We find that error vectors leading to decoding failures have small maximum support intersection with elements of these sets; further, the distribution of intersections is quite similar to that of sampling random error vectors and counting the intersections with \(\mathcal {C}\), \(\mathcal {N}\), and \(2\mathcal {N}\). Our results indicate that these three sets are not sufficient in classifying vectors expected to cause decoding failures. Finally, we study the role of syndrome weight on the decoding behavior and conclude that the set of error vectors that lead to decoding failures differ from random vectors by having low syndrome weight.KeywordsBIKEError-correcting codesMcEliecePQCQC-MDPC

This paper addresses the problem of top-k inner product join, which, given two sets of high-dimensional vectors and a result size k, outputs k pairs of vectors that have the largest inner product. This problem has important applications, such as recommendation, information extraction, and finding outlier correlation. Unfortunately, computing the exact answer incurs an expensive cost for large high-dimensional datasets. We therefore consider an approximate solution framework that efficiently retrieves k pairs of vectors with large inner products. To exploit this framework and obtain an accurate answer, we extend a state-of-the-art proximity graph for inner product search. We conduct experiments on real datasets, and the results show that our solution is faster and more accurate than baselines with state-of-the-art techniques.

Let (X1, ..., Xn) be a random vector with independent components. It is proven in this paper that, under certain restrictions, the distributions of the pairS1=sup (a1X1, ..., anXn) andS2=sup (b1X1,...,bnXn) univocally define the distribution function of the components Xj.

Remarks on univariate elliptical distributions

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

A robust predictive approach for canonical correlation analysis

We seek the maximum number of users possible for multiuser, spread-spectrum radio systems, as the signal set is varied, under the following ideal conditions: 1) no fading; 2) synchronous system; 3) orthogonal signal set for each user; 4) matched-filter individual receivers; 5) no additive noise. Welch has given an upper bound on the number of vectors (or equivalently signals) w possible in a d -dimensional space, given the maximum cross-correlation magnitude C max between any vector pair. However, the error rate for the systems under study may depend on a suitably defined root-mean-square cross correlation C rms , rather than on the maximum cross correlation Cmax of a vector set. We extend Welch's results to d -dimensional vector sets of size w divided into alphabets of size A , the vectors of each alphabet being strictly orthogonal, and give the maximum size of such a vector set as function of C rms . We demonstrate that as Welch's limit is approached, all cross correlations must approach C max , and given precise limits on the way in which this must occur. Similarly, close to the present bounds (in terms of C rms ) all rms cross correlations must be close to C rms . Particular examples are given of signal sets close to the present bounds.

It is shown that under suitable regularity conditions, differential entropy is O(√n)-Lipschitz as a function of probability distributions on ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) Shannon entropy is shown to be O(n)-Lipschitz in distributions over the product space with respect to Ornstein's d̅-distance (Wasserstein distance corresponding to the Hamming distance). These results together with Talagrand's and Marton's transportation-information inequalities allow one to replace the unknown multi-user interference with its i.i.d. approximations. As an application, a new outer bound for the two-user Gaussian interference channel is proved, which, in particular, settles the “missing corner point” problem of Costa (1985).

Automated biomedical signal processing becomes an essential process to determine the indicators of diseased states. At the same time, latest developments of artificial intelligence (AI) techniques have the ability to manage and analyzing massive amounts of biomedical datasets results in clinical decisions and real time applications. They can be employed for medical imaging; however, the 1D biomedical signal recognition process is still needing to be improved. Electrocardiogram (ECG) is one of the widely used 1-dimensional biomedical signals, which is used to diagnose cardiovascular diseases. Computer assisted diagnostic models find it difficult to automatically classify the 1D ECG signals owing to time-varying dynamics and diverse profiles of ECG signals. To resolve these issues, this study designs automated deep learning based 1D biomedical ECG signal recognition for cardiovascular disease diagnosis (DLECG-CVD) model. The DLECG-CVD model involves different stages of operations such as pre-processing, feature extraction, hyperparameter tuning, and classification. At the initial stage, data pre-processing takes place to convert the ECG report to valuable data and transform it into a compatible format for further processing. In addition, deep belief network (DBN) model is applied to derive a set of feature vectors. Besides, improved swallow swarm optimization (ISSO) algorithm is used for the hyperparameter tuning of the DBN model. Lastly, extreme gradient boosting (XGBoost) classifier is employed to allocate proper class labels to the test ECG signals. In order to verify the improved diagnostic performance of the DLECG-CVD model, a set of simulations is carried out on the benchmark PTB-XL dataset. A detailed comparative study highlighted the betterment of the DLECG-CVD model interms of accuracy, sensitivity, specificity, kappa, Mathew correlation coefficient, and Hamming loss.

Given a set of high dimensional binary vectors and a similarity function (such as Jaccard and Cosine), we study the problem of finding all pairs of vectors whose similarity exceeds a given threshold. The solution to this problem is a key component in many applications with feature-rich objects, such as text, images, music, videos, or social networks. In particular, there are many important emerging applications that require the use of relatively low similarity thresholds.We propose ATLAS, a probabilistic similarity search algorithm that in expectation finds a 1 - δ fraction of all similar vector pairs. ATLAS uses truly random permutations both to filter candidate pairs of vectors and to estimate the similarity between vectors. At a 97.5% recall rate, ATLAS consistently outperforms all state-of-the-art approaches and achieves a speed-up of up to two orders of magnitude over both exact and approximate algorithms.

Assume that a natural cyclic phenomenon has been measured, but the data is corrupted by errors. The type of corruption is application-dependent and may be caused by measurements errors, or natural features of the phenomenon. This paper studies the problem of recovering the correct cycle from data corrupted by various error models, formally defined as the period recovery problem. Specifically, we define a metric property which we call pseudo-locality and study the period recovery problem under pseudo-local metrics. Examples of pseudo-local metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudo-local metrics, periodicity is a powerful property allowing detecting the original cycle and correcting the data, under suitable conditions. Some surprising features of our algorithm are that we can efficiently identify the period in the corrupted data, up to a number of possibilities logarithmic in the length of the data string, even for metrics whose calculation is \({\cal NP}\) -hard. For the Hamming metric we can reconstruct the corrupted data in near linear time even for unbounded alphabets. This result is achieved using the property of separation in the self-convolution vector and Reed-Solomon codes. Finally, we employ our techniques beyond the scope of pseudo-local metrics and give a recovery algorithm for the non pseudo-local Levenshtein edit metric.KeywordsEdit DistanceRecovery AlgorithmSubstitution ErrorCycle DetectionCorrupted DataThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Data analysis typically involves error recovery and detection of regularities as two different key tasks. In this paper we show that there are data types for which these two tasks can be powerfully combined. A common notion of regularity in strings is that of a cover. Data describing measures of a natural coverable phenomenon may be corrupted by errors caused by the measurement process, or by the inexact features of the phenomenon itself. Due to this reason, different variants of approximate covers have been introduced, some of which are NP-hard to compute. In this paper we assume that the Hamming distance metric measures the amount of corruption experienced, and study the problem of recovering the correct cover from data corrupted by mismatch errors, formally defined as the cover recovery problem (CRP). We show that for the Hamming distance metric, coverability is a powerful property allowing detecting the original cover and correcting the data, under suitable conditions. We also study a relaxation of another problem, which is called the approximate cover problem (ACP). Since the ACP is proved to be NP-hard [Amir,Levy,Lubin,Porat, CPM 2017], we study a relaxation, which we call the candidate-relaxation of the ACP, and show it has a polynomial time complexity. As a result, we get that the ACP also has a polynomial time complexity in many practical situations. An important application of our ACP relaxation study is also a polynomial time algorithm for the cover recovery problem (CRP).