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

Apr 11, 2023 •345 likes •413 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

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 University 1 / 3
Probabilistic Models Smoker ( S ) Asthma ( A ) Cough ( C ) Let q = Pr[Asthma( A ) | Cough( C )] Pr[Event | Evidence] 2 / 3
Probabilistic Models Smoker ( S ) Asthma ( A ) Cough ( C ) Let q = Pr[Asthma( A ) | Cough( C )] Pr[Event | Evidence] #P-Hard to compute, so need for relaxations 2 / 3
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) 3 / 3
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 3 / 3
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. 3 / 3

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