Resolution Limits of Non-Adaptive Querying for Noisy 20 Questions - PowerPoint PPT Presentation

Resolution Limits of Non-Adaptive Querying for Noisy 20 Questions Estimation Lin Zhou EECS Department, University of Michigan Joint work with Prof. Alfred Hero Paper 1043, ISIT 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 1 / 15

Origin: 20 Questions Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 2 / 15

Origin: 20 Questions Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 2 / 15

Origin: 20 Questions Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 2 / 15

Origin: 20 Questions Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 2 / 15

Origin: 20 Questions Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 2 / 15

System Model: Searching with Noise Queries ❄ Answers ✲ Responder ✲ Questioner ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Target: estimate a continuous random variable S with pdf f S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 3 / 15

System Model: Searching with Noise Queries ❄ Answers ✲ Responder ✲ Questioner ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Target: estimate a continuous random variable S with pdf f S Task: design queries and decoder (scheme/strategy/policy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 3 / 15

System Model: Searching with Noise Queries ❄ Answers ✲ Responder ✲ Questioner ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Target: estimate a continuous random variable S with pdf f S Task: design queries and decoder (scheme/strategy/policy) Motivation: applications such as localization with sensor networks, human brain interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 3 / 15

Adaptive and Non-Adaptive Query Schemes A query asks whether S lies in a certain set Q ⊂ [ 0 , 1 ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 4 / 15

Adaptive and Non-Adaptive Query Schemes A query asks whether S lies in a certain set Q ⊂ [ 0 , 1 ] Query schemes can be classified as adaptive and non-adaptive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 4 / 15

Adaptive and Non-Adaptive Query Schemes A query asks whether S lies in a certain set Q ⊂ [ 0 , 1 ] Query schemes can be classified as adaptive and non-adaptive Adaptive Y 1 , . . . , Y i − 1 Q i ✛ Q 1 , . . . , Q i − 1 ❄ S ✲ Oracle X i ❄ Noisy Channel Y i ❄ Decoder Stop ❄ ˆ S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 4 / 15

Adaptive and Non-Adaptive Query Schemes A query asks whether S lies in a certain set Q ⊂ [ 0 , 1 ] Query schemes can be classified as adaptive and non-adaptive Adaptive Non-adaptive Y 1 , . . . , Y i − 1 Q i Q 1 Q 2 Q n ✛ r r r Q 1 , . . . , Q i − 1 ❄ ❄ ❄ ❄ S S ✲ Oracle ✲ Oracle X i X 1 X 2 X n r r r ❄ ❄ ❄ ❄ Noisy Channel Noisy Channel Y i Y 1 Y 2 Y n r r r ❄ ❄ ❄ ❄ Decoder Decoder Stop ❄ ˆ ❄ S ˆ S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 4 / 15

Measurement Independent and Dependent 12 Noise Measurement independent noise Q i ❄ X i Y i ✲ Oracle P Y | X S ✲ ✲ 1 Y. Kaspi, O. Shayevitz, and T. Javidi, “Searching with measurement dependent noise,” IEEE Trans. Inf. Theory, vol. 64, no. 4, pp. 2690-2705, 2018. 2 A. Lalitha, N. Ronquillo, and T. Javidi, “Improved target acquisition rates with feedback codes,” IEEE . . . . . . . . . . . . . . . . . . . . Journal of Selected Topics in Signal Processing, vol. 12, no. 5, pp. 871-885, 2018. . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 5 / 15

Measurement Independent and Dependent 12 Noise Measurement independent noise Measurement dependent noise Q i Q i ❄ ❄ ❄ X i Y i X i Y i ✲ Oracle ✲ Oracle P |Q i | P Y | X S S ✲ ✲ ✲ ✲ Y | X 1 Y. Kaspi, O. Shayevitz, and T. Javidi, “Searching with measurement dependent noise,” IEEE Trans. Inf. Theory, vol. 64, no. 4, pp. 2690-2705, 2018. 2 A. Lalitha, N. Ronquillo, and T. Javidi, “Improved target acquisition rates with feedback codes,” IEEE . . . . . . . . . . . . . . . . . . . . Journal of Selected Topics in Signal Processing, vol. 12, no. 5, pp. 871-885, 2018. . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 5 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise Excess-resolution probability with respect to a tolerable resolution level δ ∈ R + Pr {| ˆ sup S − S | > δ } f S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise Excess-resolution probability with respect to a tolerable resolution level δ ∈ R + Pr {| ˆ sup S − S | > δ } f S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise Excess-resolution probability with respect to a tolerable resolution level δ ∈ R + Pr {| ˆ sup S − S | > δ } f S Analogous to excess-distortion probability in rate-distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise Excess-resolution probability with respect to a tolerable resolution level δ ∈ R + Pr {| ˆ sup S − S | > δ } f S Analogous to excess-distortion probability in rate-distortion Probably approximately correct learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15

Problem Formulation Queries ❄ ❄ Answers ✲ Oracle ✲ Decoder ✲ ˆ S ∈ [ 0 , 1 ] Noisy Channel ✲ S Searching with measurement dependent noise Excess-resolution probability with respect to a tolerable resolution level δ ∈ R + Pr {| ˆ sup S − S | > δ } f S Analogous to excess-distortion probability in rate-distortion Probably approximately correct learning Similar to the criterion considered in Kaspi et al. , TIT 2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lin Zhou (University of Michigan) ISIT 2020 Paper 1043: Noisy 20 Questions 6 / 15