Sum of squares

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11Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Grothendieck-type inequalities Suppose A ∈ Rn×m is a linear operator from Rm to Rn represented

Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Grothendieck-type inequalities Suppose A ∈ Rn×m is a linear operator from Rm to Rn represented

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Source URL: sumofsquares.org

- Date: 2016-11-17 19:44:26
    12Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Application: Sparse coding / dictionary learning The dictionary learning / sparse coding problem is defined as follows:

    Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Application: Sparse coding / dictionary learning The dictionary learning / sparse coding problem is defined as follows:

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    - Date: 2016-11-17 19:44:26
      13HomeworkProve that 15x2 − 7y 2 = 16 has no solutions in Z. 2. Prove that an integer of the form 8n + 7 cannot be written as a sum of three integer squares. 3. Show that if x2 = a is solvable modulo p then it is

      HomeworkProve that 15x2 − 7y 2 = 16 has no solutions in Z. 2. Prove that an integer of the form 8n + 7 cannot be written as a sum of three integer squares. 3. Show that if x2 = a is solvable modulo p then it is

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      Source URL: www.math.nyu.edu

      - Date: 2016-09-07 16:50:49
        14Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Optimality of sum-of-squares In this lecture, we show that sum-of-squares achieves the best possible approximation guarantees for every constraint sati

        Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Optimality of sum-of-squares In this lecture, we show that sum-of-squares achieves the best possible approximation guarantees for every constraint sati

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        Source URL: sumofsquares.org

        - Date: 2016-11-30 18:56:07
          15Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Mathematical Definitions Let us now turn to formally defining the problem of polynomial

          Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Mathematical Definitions Let us now turn to formally defining the problem of polynomial

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          Source URL: www.sumofsquares.org

          - Date: 2016-11-17 19:44:26
            16Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Cheeger’s inequality Let G be a d-regular graph with vertex set V = [n]. For a vertex

            Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Cheeger’s inequality Let G be a d-regular graph with vertex set V = [n]. For a vertex

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            Source URL: sumofsquares.org

            - Date: 2016-11-17 19:44:26
              17Proof, beliefs, and algorithms through the lens of sum-of-squares 1 An integrality gap for the planted clique problem The Planted Clique problem (sometimes referred to as the hidden clique

              Proof, beliefs, and algorithms through the lens of sum-of-squares 1 An integrality gap for the planted clique problem The Planted Clique problem (sometimes referred to as the hidden clique

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              Source URL: sumofsquares.org

              - Date: 2016-11-17 19:44:26
                18Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Introduction The terms “Algebra” and “Algorithm” both originate from the same

                Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Introduction The terms “Algebra” and “Algorithm” both originate from the same

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                Source URL: www.sumofsquares.org

                - Date: 2016-11-17 19:44:26
                  19Proof, beliefs, and algorithms through the lens of sum-of-squares 1 From integrality gaps to hardness We have seen how we can transform computational hardness results into integrality gaps. In a surprising work Raghaven

                  Proof, beliefs, and algorithms through the lens of sum-of-squares 1 From integrality gaps to hardness We have seen how we can transform computational hardness results into integrality gaps. In a surprising work Raghaven

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                  Source URL: sumofsquares.org

                  - Date: 2016-11-17 19:44:26
                    20Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Is sos an “optimal algorithm”? We have alluded several times in this course to the intuition that sum

                    Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Is sos an “optimal algorithm”? We have alluded several times in this course to the intuition that sum

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                    Source URL: sumofsquares.org

                    - Date: 2016-11-17 19:44:26