Detecting **Low**-**Complexity** Confounders from Data
Maria Virginia Ruiz Cuevas 1 2 Nataliya Sokolovska 1 Pierre-Henri Wuillemin 3 Jean-Daniel Zucker 4
Abstract
Statistical dependencies between two variables X and Y indicate that either X causes Y , or Y causes X, or there exists a latent variable Z which influences X and Y . In biology and medicine, an important problem is to find genetic or environ- mental unobserved causes of phenotypic differ- ence between individuals. In this contribution, we introduce a novel approach to identify unobserved confounders in data. The proposed method is based on the state-of-the-art 3off2 causal network reconstruction algorithm, and on an evidence for a direct causal relation represented by purity of con- ditionals. The proposed method is implemented in Python, and it will be publicly available shortly. We discuss the results obtained on a real biomedi- cal dataset.

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In this work we propose a **low** **complexity** DFD algo- rithm for large WSNs. Our approach differs with respect to classical solutions in the fact that the comparison of the local and neighboring measurements in the first phase of the algorithm only determines whether an outlier is present in the measurement set. This is usually an easier task than attempting to identify it. Consider, for example, three sensors measuring some constant temperature, e.g., with actual value t = 20 ◦ C. Suppose that a non-defective sensor has a bounded measurement error, e.g., ±1 degree. Assume that the local measurement of the first sensor is t 1 = 19.5 ◦ C, and that two

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The main contributions of this letter are: (i) the introduction of a new **low**-**complexity** solution for multi-tag deployment of UWB-RFID systems which avoids the use of a dedicated synchronization channel and an extensive code acquisition; (ii) the presentation of the first practical test-bed showing the real- time detection and ranging of moving UWB-RFID tags in a real application context. The rest of the letter is organized as follows. In Sec. II the UWB-RFID system architecture is re- visited; in Sec. III-A the proposed tag code assignment strategy is presented; finally, Sec. IV shows the experimental results obtained in a multi-tag scenario.

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Image domain Voronoi partition Kinetic partition Image domain + simulated annealing
Figure 3. Initialization. The top (resp. bottom) row shows the initial partitions (resp. output polygons). Objects of interest are persons and bikes. Starting the exploration mechanism from a partition composed of one rectangular facet (column 1) typically produces results with missing objects such as the bike. An initial Voronoi partition [ 11 ] (column 2) is too fragmented to output **low** **complexity** polygons. Our algorithm performs best from kinetic partitions [ 3 ] (column 3) with a good trade-off between accuracy and polygon **complexity**. This option returns similar results than a simulated annealing exploration (column 4) but with processing times reduced by two orders of magnitude. For clarity reasons, here and in the following figures, we do not display the background polygons (at the image border) in the visual results.

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To avoid the shortcomings of aforementioned methods (high SNR performance limitation for LMMSE, limitation on the spacing/number of pilots for the others), we use the finite delay spread of the channel and develop a **low**-**complexity** algorithm capable of estimating the channel from part of the carriers only. We introduce a deterministic model and derive the associated maximum-likelihood (ML) estimator. This ML estimator can be interpreted as a transformation from frequency domain to time domain and back to frequency. The actual estimation is done in the time domain, where the number of parameters (i.e., the channel length) is small. The estimator is obtained by min- imizing a quadratic criterion, which, combined with the small number of parameters, leads to a **low**-**complexity** algorithm. As such, we have obtained an exact **low**-**complexity** solution. We extend our approach to pilot symbol-assisted modulation (PSAM) and link it to the constrained least squares (CLS) solution proposed in [3]. It is worth noting that although our estimator is based on a parametric model, the only parameter is the channel length (by channel, we mean the concatenation of the front-end filters and the propagation channel). The only condition is then that the global channel length (which can be significantly longer than the propagation channel itself) has to be smaller than this one parameter. As a result, the method is rather robust against channel modeling errors, the main disadvantage being that the length parameter of the ML estimator can be rather large, leading to a loss in performance.

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In this letter, we derive an exact **low**-**complexity** MMSE-FDE based on the FS representation of the CPM wave- forms, only considering time-invariant frequency-selective channels. As in [2], we perform a linear MMSE-FDE over the over-sampled complex envelope of the CPM signals, but by using the FS representation, we can fully benefit from the properties of circular block-based CPM and reduce the **complexity**, without making any kind of approximation in the equalizer derivation. While performing the same as the equalizer proposed by Pancaldi and Vitetta [1] and the “full **complexity**” polyphase domain equalizer of Thillo et al. [2], we will show that the proposed approach has a significant lower **complexity**, of the same order as the approximated **low**

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Route de Villejust, 91620 Nozay, France
Abstract
This paper describes a single-image super-resolution (SR) algorithm based on non- negative neighbor embedding. It belongs to the family of single-image example-based SR algorithms, since it uses a dictionary of **low** resolution (LR) and high resolution (HR) trained patch pairs to infer the unknown HR details. Each LR feature vector in the input image is expressed as the weighted combination of its K nearest neighbors in the dictio- nary; the corresponding HR feature vector is reconstructed under the assumption that the local LR embedding is preserved. Three key aspects are introduced in order to build a **low**-**complexity** competitive algorithm: (i) a compact but efficient representation of the patches (feature representation) (ii) an accurate estimation of the patches by their near- est neighbors (weight computation) (iii) a compact and already built (therefore external) dictionary, which allows a one-step upscaling. The neighbor embedding SR algorithm so designed is shown to give good visual results, comparable to other state-of-the-art methods, while presenting an appreciable reduction of the computational time.

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In this paper, we present a **low** **complexity** decoupled multiuser ranging (DEMR) estimator for TOA estimation in direct-sequence ultra-wideband (DS-UWB) ranging system. DEMR estimator extends DEMA algorithm [15] into DS- UWB ranging system. With the assumption that TOA is the integer multiples of chip duration, we replace the MF in [15] by an integrate-and-dump filter (IDF) in chip sampling rate to reduce the sampling rate and to simplify the estimator structure. Moreover, comparing with the work of [15], this subsampling TOA estimator is simplified substantially in mul- tipath environment due to the long repetition time of DS- UWB pulse. Searching over a multi-dimensional parameter space problem is simplified to a set of one-dimensional (1- D) problems. Although reducing **complexity** considerably, we show that DEMR estimator is quite near-far resistant and can obtain noticeable performance in fully-loaded system in the dense multipath channel.

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7 Conclusion
The 3D MIMO code has been shown to be efficient and robust in distributed MIMO scenarios. Yet, it suffers from high ML decoding **complexity**. In this paper, we first proposed a new form of the 3D MIMO codeword and investigated some important properties of the new codeword. With these properties, the 3D MIMO code is proved to be fast decodable. Consequently, we proposed a reduced-**complexity** ML decoder for the 3D MIMO code which offers the same performance as ML decoder. Simulation results demonstrate that the novel **low**-**complexity** decoder yields much less processing time latency than the classical Guo-Nilson’s sphere decoder with Schnorr-Euchner enumeration. Moreover, the proposed 2-by-2 column switch technique can significantly reduce the average decoding **complexity**, especially with 16-QAM modulation.

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2.2. ASR-based enhancement layer encoder
The local adaptation of the spatial resolution is at the heart of the proposed **low**-**complexity** EL encoder. Indeed, since natural im- ages/videos comprise locally variant spatial frequency components, it can be beneficial to adjust the sampling rate at a block level to per- form a down/upsampling based encoding [9, 10]. The proposed EL encoder allows for different combinations of horizontal and vertical sampling rates of 1 and 1/2, achieved by successive 1D downsam- plings of the EL input block. This leads to the set of possible reso- lution modes L = {2N×2N, N×2N, 2N×N, N×N}, with N the width of the square block in BL resolution, and W×H referring to an EL block coding spatial resolution of width W and height H.

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In the remainder of the introduction we shall give an overview of the model and contributions. Then, in the ensuing section, we provide a very thorough discussion of the related works.
We consider continuous and discrete models with caches located at arbitrary locations either in the plane or in the grid. Caches know their own coverage area as well as the coverage areas of other caches that overlap with this region. There is a content catalog from which users request files according to a known probability distribution. Each cache can store a limited number of files and the goal is to minimize the probability that a user at an arbitrary location in the plane will not find the file that she requires in one of the caches that she is covered by. We develop **low**-**complexity** asynchronous distributed cooperative content placement caching algorithms that require communication only between caches with overlapping coverage areas. In the basic algorithm, at each iteration a cache will selfishly update its cache content by minimizing the local miss probability and by considering the

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In this paper, we propose algorithms for PCA and MCA prob- lems with **low** **complexity** and improved convergence perfor- mance. 1 These algorithms are based on the Orthogonal Projec- tion Approximation and Subspace Tracking (OPAST) algorithm [27] , originally introduced for Principal Subspace Analysis (PSA). In [28] , authors propose to use jointly OPAST algorithm and a diagonal- ization technique using Givens rotations to achieve the PCA. The resulting algorithm shows good performance but suffers from ill convergence when the system’s dimensions increase or the num- ber of principal components is large. To improve its performance in the large dimensional context, we propose herein different algo- rithm’s versions using different selection procedures of the Givens rotation indices. A comparative study shows that the best algorith- m’s version (in terms of convergence rate and estimation accuracy) is the one associated to the hybrid selection method shown in Sec- tion 3.2.1 .

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In this letter, we derive an exact **low**-**complexity** MMSE-FDE based on the FS representation of the CPM wave- forms, only considering time-invariant frequency-selective channels. As in [2], we perform a linear MMSE-FDE over the over-sampled complex envelope of the CPM signals, but by using the FS representation, we can fully benefit from the properties of circular block-based CPM and reduce the **complexity**, without making any kind of approximation in the equalizer derivation. While performing the same as the equalizer proposed by Pancaldi and Vitetta [1] and the “full **complexity**” polyphase domain equalizer of Thillo et al. [2], we will show that the proposed approach has a significant lower **complexity**, of the same order as the approximated **low**

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V. C ONCLUSION
In this paper, we have compared two solutions for the **complexity** reduction of LMMSE in OFDM/OQAM. A first approximation (labeled as Approximation-1 ) was originally designed for the OFDM modulation [7], and was used in OFDM/OQAM in [6]. The prpoposed second approximation (labeled as Approximation-2 ) in this paper is more adapted to OFDM/OQAM, since the circulant feature of the noise covariance matrix is taken into account in the LMMSE ap- proximation. The results revealed that both proposed approxi- mations have very similar performances, but Approximation-1 is more complex than Approximation-2 . As a consequence, we can conclude that the proposed Approximation-2 is a very good candidate for **low**-**complexity** LMMSE estimation in OFDM/OQAM.

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Local Linear Convergence of Douglas–Rachford/ADMM for **Low** **Complexity** Regularization
Jingwei Liang ∗ , Jalal M. Fadili ∗ , Gabriel Peyr´e † and Russell Luke ‡
∗ GREYC, CNRS, ENSICAEN, Universit´e de Caen, Email: {Jingwei.Liang, Jalal.Fadili}@ensicaen.fr † CNRS, Ceremade, Universit´e Paris-Dauphine, Email: Gabriel.Peyre@ceremade.dauphine.fr

ALOHA medium access protocol quickly become interference limited when node density increases, thus necessitating new interference-related performance metrics [2].
The present work focuses on the design of a **low** **complexity**, real-time interference detector for LPWA transceivers. Our objective is that, every time the transceiver correctly receives a frame, the detector simultaneously outputs information on the presence or absence of interference, and, if applicable, information concerning the interference’s relative strength and duration. This interference-related information gathered by the wireless node can be used in many ways. An obvious application is network planning and selection of base station installation sites. Indeed, since the information is gathered by the nodes themselves, the network installer will dispose of very precise information concerning congested areas and be able to optimize the base station placement accordingly. Alternatively, interference-related information can be used by adaptive transmission protocols that aim to optimize the physi- cal layer signalling rate in view of either improving throughput or saving energy when favourable RF propagation conditions have been detected. Detailed per-frame interference-related information can be exploited to fine-tune channel adaptation strategies.

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simplify procedure-2 so as to bring down the number of compare and save operations to a more reasonable value. In a first attempt, we tried to reduce q and we observed that the degradation in coding gain was relatively small for q�8. On the other hand, for q<8 we observed an important degradation of the coding gain as we reduced q. Thus we are limited to q=8 for coding gain considerations and the average decoding **complexity** for one column is only divided by a factor 2. Next, we tried to reduce the **complexity** of procedure-2. For this we tried to find an easy way to identify code word C without going through the search procedure. W e found that we could considerably reduce Q2, with a small coding gain de gradation, by replacing code word C by decision D(m-1) when computing the extrinsic information W(m+l). This is the main breakthrough which led to the new **low** **complexity** block turbo decoder.

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In this paper, a novel **low** **complexity** hierarchical synchro- nization method is proposed. A new training symbol which has both repeating patterns and conjugate symmetry property is used. The training symbol is based on modified Chu (CAZAC) [9] sequence, which has smaller alphabet size than Zadoff-Chu sequences. The hierarchical timing metric proposed uses delay correlation in the first step and conjugate symmetry correlation in the second step. The first step is computationally efficient and operates on larger number of samples, while second step is computationally expensive but operates on fixed number of samples. The hierarchical method gains **complexity** advantage and good MSE performance by the auto-correlation (first step) and cross-correlation (second step) respectively.

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in equation (2) (respectively α (m) in equation (3)). [6] considers parallel rows and columns
decoding of the product code in order to half the latency of the decoder. [7] presents a **low**- **complexity** Chase decoder.
The purpose of this letter is to show that it is absolutely unnecessary to put any of the Chase codewords into memory and that at each iteration, one can readily update the output of the SISO decoder.