On the Hardness of Probabilistic Inference Relaxations Supratik - - PowerPoint PPT Presentation

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Apr 11, 2023 345 likes •415 views

On the Hardness of Probabilistic Inference Relaxations Supratik Chakraborty 1 Kuldeep S. Meel 2 Moshe Y. Vardi 3 1 Indian Institute of Technology, Bombay 2 School of Computing, National University of Singapore 3 Department of Computer Science, Rice

SLIDE 1

On the Hardness of Probabilistic Inference Relaxations

Supratik Chakraborty1 Kuldeep S. Meel2 Moshe Y. Vardi3

1Indian Institute of Technology, Bombay 2School of Computing, National University of Singapore 3Department of Computer Science, Rice University 1 / 3

SLIDE 2

Probabilistic Models

Smoker (S) Cough (C) Asthma (A) Let q = Pr[Asthma(A) | Cough(C)] Pr[Event | Evidence]

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SLIDE 3

Probabilistic Models

Smoker (S) Cough (C) Asthma (A) Let q = Pr[Asthma(A) | Cough(C)] Pr[Event | Evidence] #P-Hard to compute, so need for relaxations

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SLIDE 4

The Story of Relaxations with a Moral Conclusion

Let q = Pr[Event | Evidence]

Additive Relaxations

Given: δ, ε Estimate r such that Pr[q − ε < r < q + ε] ≥ 1 − δ (Sarkhel et al. 2016); (Fink,Huang, and Olteanu 2013)

Threshold Relaxations

Given: thresh, δ if r ≥ thresh, then textbfOutput YES, else textbfOutput NO (Moy´ e 2006; King, Rosopa, and Minium 2010; Zongming 2009; Gordon et al. 2014; Bornholt, Mytkowicz, and McKinley 2014)

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SLIDE 5

The Story of Relaxations with a Moral Conclusion

Let q = Pr[Event | Evidence]

Additive Relaxations

Given: δ, ε Estimate r such that Pr[q − ε < r < q + ε] ≥ 1 − δ (Sarkhel et al. 2016); (Fink,Huang, and Olteanu 2013)

Threshold Relaxations

Given: thresh, δ if r ≥ thresh, then textbfOutput YES, else textbfOutput NO (Moy´ e 2006; King, Rosopa, and Minium 2010; Zongming 2009; Gordon et al. 2014; Bornholt, Mytkowicz, and McKinley 2014) The proposed relaxations are as hard as computing q exactly

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SLIDE 6

The Story of Relaxations with a Moral Conclusion

Let q = Pr[Event | Evidence]

Additive Relaxations

Given: δ, ε Estimate r such that Pr[q − ε < r < q + ε] ≥ 1 − δ (Sarkhel et al. 2016); (Fink,Huang, and Olteanu 2013)

Threshold Relaxations

Given: thresh, δ if r ≥ thresh, then textbfOutput YES, else textbfOutput NO (Moy´ e 2006; King, Rosopa, and Minium 2010; Zongming 2009; Gordon et al. 2014; Bornholt, Mytkowicz, and McKinley 2014) The proposed relaxations are as hard as computing q exactly Not all is lost. New Relaxation that is efficient to compute and can replace threshold relaxation for statistical testing applications Money Back Guarantee: Come to the poster tonight, and you will leave demanding a rigorous analysis everytime someone proposes new relaxation.

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