On L1q Regularized Regression

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On L1q Regularized Regression

• Authors Han Liu and Jian Zhang
• Presented by Jun Liu

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Problem (1)
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Problem (2)
The number of groups is much larger than the
number of samples
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Outline

• Proposition 2.1, 2.2
  (Subgradient, linearly dependent)
• Definition 2.4-2.7 (Properties to
  be established)
• Theorem 3.1
  (Variable Selection Consistency)
• Lemma 4.1
  (Technical lemma)
• Assumption 1, Theorem 4.3 (Consistency, linear
  model)
• Assumption 2. Theorem 4.5 (Inequality,
  misspecified model)
• Assumption 4, Theorem 5.1 (Risk consistency)

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Outline

• Proposition 2.1, 2.2
  (Subgradient, linear dependent)
• Definition 2.4-2.7 (Properties to
  be established)
• Theorem 3.1
  (Variable Selection Consistency)
• Lemma 4.1
  (Technical lemma)
• Assumption 1, Theorem 4.3 (Consistency, linear
  model)
• Assumption 2. Theorem 4.5 (Inequality,
  misspecified model)
• Assumption 4, Theorem 5.1 (Risk consistency)

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Outline

• Proposition 2.1, 2.2
  (Subgradient, linear dependent)
• Definition 2.4-2.7 (Properties to
  be established)
• Theorem 3.1 (Variable
  Selection Consistency)
• Lemma 4.1
  (Technical lemma)
• Assumption 1, Theorem 4.3 (Consistency, linear
  model)
• Assumption 2. Theorem 4.5 (Inequality,
  misspecified model)
• Assumption 4, Theorem 5.1 (Risk consistency)

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Key Points in the Proof

• Objective
• Two parts
• Tools

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Part 1
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Part 1
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Part 1
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Part 2
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Part 2
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Part 2
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Outline

• Proposition 2.1, 2.2
  (Subgradient, linear dependent)
• Definition 2.4-2.7 (Properties to
  be established)
• Theorem 3.1
  (Variable Selection Consistency)
• Lemma 4.1
  (Technical lemma)
• Assumption 1, Theorem 4.3 (Consistency, linear
  model)
• Assumption 2. Theorem 4.5 (Inequality,
  misspecified model)
• Assumption 4, Theorem 5.1 (Risk consistency)

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Outline

• Proposition 2.1, 2.2
  (Subgradient, linear dependent)
• Definition 2.4-2.7 (Properties to
  be established)
• Theorem 3.1
  (Variable Selection Consistency)
• Lemma 4.1
  (Technical lemma)
• Assumption 1, Theorem 4.3 (Consistency, linear
  model)
• Assumption 2. Theorem 4.5 (Inequality,
  misspecified model)
• Assumption 4, Theorem 5.1 (Risk consistency)