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Homomorphic Sensing Manolis C. T sakiris Liangzu Peng ShanghaiT ech University <latexit

  1. Homomorphic Sensing Manolis C. T sakiris Liangzu Peng ShanghaiT ech University

  2. <latexit sha1_base64="+a9H+R06Yv8T41qcam0W1mUv46g=">AB7XicbVBNSwMxEJ34WetX1aOXYBE8lV0R9CJUvHiSCvYD2qVk02wbm02WJCuWpf/BiwdFvPp/vPlvTNs9aOuDgcd7M8zMCxPBjfW8b7S0vLK6tl7YKG5ube/slvb2G0almrI6VULpVkgME1yuVWsFaiGYlDwZrh8HriNx+ZNlzJeztKWBCTvuQRp8Q6qXH1hC9x2C2VvYo3BV4kfk7KkKPWLX1eoqmMZOWCmJM2/cSG2REW04FGxc7qWEJoUPSZ21HJYmZCbLptWN87JQejpR2JS2eqr8nMhIbM4pD1xkTOzDz3kT8z2unNroIMi6T1DJZ4uiVGCr8OR13OaUStGjhCqubsV0wHRhFoXUNGF4M+/vEgapxXfq/h3Z+XqbR5HAQ7hCE7Ah3Oowg3UoA4UHuAZXuENKfSC3tHrHUJ5TMH8Afo8wdbKY5a</latexit> <latexit sha1_base64="+a9H+R06Yv8T41qcam0W1mUv46g=">AB7XicbVBNSwMxEJ34WetX1aOXYBE8lV0R9CJUvHiSCvYD2qVk02wbm02WJCuWpf/BiwdFvPp/vPlvTNs9aOuDgcd7M8zMCxPBjfW8b7S0vLK6tl7YKG5ube/slvb2G0almrI6VULpVkgME1yuVWsFaiGYlDwZrh8HriNx+ZNlzJeztKWBCTvuQRp8Q6qXH1hC9x2C2VvYo3BV4kfk7KkKPWLX1eoqmMZOWCmJM2/cSG2REW04FGxc7qWEJoUPSZ21HJYmZCbLptWN87JQejpR2JS2eqr8nMhIbM4pD1xkTOzDz3kT8z2unNroIMi6T1DJZ4uiVGCr8OR13OaUStGjhCqubsV0wHRhFoXUNGF4M+/vEgapxXfq/h3Z+XqbR5HAQ7hCE7Ah3Oowg3UoA4UHuAZXuENKfSC3tHrHUJ5TMH8Afo8wdbKY5a</latexit> <latexit sha1_base64="+a9H+R06Yv8T41qcam0W1mUv46g=">AB7XicbVBNSwMxEJ34WetX1aOXYBE8lV0R9CJUvHiSCvYD2qVk02wbm02WJCuWpf/BiwdFvPp/vPlvTNs9aOuDgcd7M8zMCxPBjfW8b7S0vLK6tl7YKG5ube/slvb2G0almrI6VULpVkgME1yuVWsFaiGYlDwZrh8HriNx+ZNlzJeztKWBCTvuQRp8Q6qXH1hC9x2C2VvYo3BV4kfk7KkKPWLX1eoqmMZOWCmJM2/cSG2REW04FGxc7qWEJoUPSZ21HJYmZCbLptWN87JQejpR2JS2eqr8nMhIbM4pD1xkTOzDz3kT8z2unNroIMi6T1DJZ4uiVGCr8OR13OaUStGjhCqubsV0wHRhFoXUNGF4M+/vEgapxXfq/h3Z+XqbR5HAQ7hCE7Ah3Oowg3UoA4UHuAZXuENKfSC3tHrHUJ5TMH8Afo8wdbKY5a</latexit> <latexit sha1_base64="+a9H+R06Yv8T41qcam0W1mUv46g=">AB7XicbVBNSwMxEJ34WetX1aOXYBE8lV0R9CJUvHiSCvYD2qVk02wbm02WJCuWpf/BiwdFvPp/vPlvTNs9aOuDgcd7M8zMCxPBjfW8b7S0vLK6tl7YKG5ube/slvb2G0almrI6VULpVkgME1yuVWsFaiGYlDwZrh8HriNx+ZNlzJeztKWBCTvuQRp8Q6qXH1hC9x2C2VvYo3BV4kfk7KkKPWLX1eoqmMZOWCmJM2/cSG2REW04FGxc7qWEJoUPSZ21HJYmZCbLptWN87JQejpR2JS2eqr8nMhIbM4pD1xkTOzDz3kT8z2unNroIMi6T1DJZ4uiVGCr8OR13OaUStGjhCqubsV0wHRhFoXUNGF4M+/vEgapxXfq/h3Z+XqbR5HAQ7hCE7Ah3Oowg3UoA4UHuAZXuENKfSC3tHrHUJ5TMH8Afo8wdbKY5a</latexit> Shuffled Linear Regression Ax = b known only up to a permutation [1] A. Pananjady, M. J. Wainwright, T . D. Courtade, “Linear regression with shuffled data: statistical and computational limits of permutation recovery”, IEEE T ransactions on Information Theory, 2018. [2] J. Unikrishnan, S. Haghighatsoar, M. Vetterli, “Unlabeled sensing with random linear measurements”, IEEE T ransactions on Information Theory, 2018. [3] M. Slawski and E. Ben-David, “Linear regression with sparsely permuted data”, Electronic Journal of Statistics, 2019. [4] X. Song, H. Choi, Y. Shi, “Permuted linear model for header-free communication via symmetric polynomials”, ISIT , 2018.

  3. <latexit sha1_base64="Gou/+BdLalt1pM2a+Bo4i0QplWQ=">ACFHicdVDLSgMxFM3UV62vUZdugq0giCUpYtdwY3uKtgHtEPJZDJtaOZBkhHK0I9w46+4caGIWxfu/BszbQUVvRByOc+jxsLrjRCH1ZuaXldS2/XtjY3NresXf32ipKJGUtGolIdl2imOAha2muBevGkpHAFazji8yvXPLpOJReKMnMXMCMgy5zynRhrYJ2enHg9YmCUQARUfzr7EVTGhDJb6AdEjSkTanpYGdhGVEUIY5gBXD1HBtTrtQquQZxJopgEc2B/d73IpqY9poKolQPo1g7KZGaU8GmhX6imBkzJkPWMzAkAVNOjtqCo8M40E/kuaFGs7Y7xUpCZSaBK7JzHZUv7WM/EvrJdqvOSkP40SzkM4H+YmAOoKZQ9DjklEtJgYQKrnZFdIRkYRq42PBmPB1KfwftCtljMr4ulJsXC3syIMDcAiOAQZV0ACXoAlagI78ACewLN1bz1aL9brPDVnLWr2wY+w3j4BjCKeiA=</latexit> <latexit sha1_base64="Gou/+BdLalt1pM2a+Bo4i0QplWQ=">ACFHicdVDLSgMxFM3UV62vUZdugq0giCUpYtdwY3uKtgHtEPJZDJtaOZBkhHK0I9w46+4caGIWxfu/BszbQUVvRByOc+jxsLrjRCH1ZuaXldS2/XtjY3NresXf32ipKJGUtGolIdl2imOAha2muBevGkpHAFazji8yvXPLpOJReKMnMXMCMgy5zynRhrYJ2enHg9YmCUQARUfzr7EVTGhDJb6AdEjSkTanpYGdhGVEUIY5gBXD1HBtTrtQquQZxJopgEc2B/d73IpqY9poKolQPo1g7KZGaU8GmhX6imBkzJkPWMzAkAVNOjtqCo8M40E/kuaFGs7Y7xUpCZSaBK7JzHZUv7WM/EvrJdqvOSkP40SzkM4H+YmAOoKZQ9DjklEtJgYQKrnZFdIRkYRq42PBmPB1KfwftCtljMr4ulJsXC3syIMDcAiOAQZV0ACXoAlagI78ACewLN1bz1aL9brPDVnLWr2wY+w3j4BjCKeiA=</latexit> <latexit sha1_base64="Gou/+BdLalt1pM2a+Bo4i0QplWQ=">ACFHicdVDLSgMxFM3UV62vUZdugq0giCUpYtdwY3uKtgHtEPJZDJtaOZBkhHK0I9w46+4caGIWxfu/BszbQUVvRByOc+jxsLrjRCH1ZuaXldS2/XtjY3NresXf32ipKJGUtGolIdl2imOAha2muBevGkpHAFazji8yvXPLpOJReKMnMXMCMgy5zynRhrYJ2enHg9YmCUQARUfzr7EVTGhDJb6AdEjSkTanpYGdhGVEUIY5gBXD1HBtTrtQquQZxJopgEc2B/d73IpqY9poKolQPo1g7KZGaU8GmhX6imBkzJkPWMzAkAVNOjtqCo8M40E/kuaFGs7Y7xUpCZSaBK7JzHZUv7WM/EvrJdqvOSkP40SzkM4H+YmAOoKZQ9DjklEtJgYQKrnZFdIRkYRq42PBmPB1KfwftCtljMr4ulJsXC3syIMDcAiOAQZV0ACXoAlagI78ACewLN1bz1aL9brPDVnLWr2wY+w3j4BjCKeiA=</latexit> <latexit sha1_base64="Gou/+BdLalt1pM2a+Bo4i0QplWQ=">ACFHicdVDLSgMxFM3UV62vUZdugq0giCUpYtdwY3uKtgHtEPJZDJtaOZBkhHK0I9w46+4caGIWxfu/BszbQUVvRByOc+jxsLrjRCH1ZuaXldS2/XtjY3NresXf32ipKJGUtGolIdl2imOAha2muBevGkpHAFazji8yvXPLpOJReKMnMXMCMgy5zynRhrYJ2enHg9YmCUQARUfzr7EVTGhDJb6AdEjSkTanpYGdhGVEUIY5gBXD1HBtTrtQquQZxJopgEc2B/d73IpqY9poKolQPo1g7KZGaU8GmhX6imBkzJkPWMzAkAVNOjtqCo8M40E/kuaFGs7Y7xUpCZSaBK7JzHZUv7WM/EvrJdqvOSkP40SzkM4H+YmAOoKZQ9DjklEtJgYQKrnZFdIRkYRq42PBmPB1KfwftCtljMr4ulJsXC3syIMDcAiOAQZV0ACXoAlagI78ACewLN1bz1aL9brPDVnLWr2wY+w3j4BjCKeiA=</latexit> Shuffled Linear Regression 4-dimensional signal subspace V 1 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 18 20 1 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 18 20 1 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 18 20 1 0.5 0 -0.5 -1 0 2 4 6 8 10 12 14 16 18 20

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