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Explaining the results of Machine learning algorithms is crucial given the rapid growth and potential applicability of these methods in critical domains including healthcare, defense, autonomous driving, etc. In this paper, we address this problem in the context of Markov Logic Networks (MLNs) which are highly expressive statistical relational models that combine first-order logic with probabilistic graphical models. MLNs in general are known to be interpretable models, i.e., MLNs can be understood more easily by humans as compared to models learned by approaches such as deep learning. However, at the same time, it is not straightforward to obtain human-understandable explanations specific to an observed inference result (e.g. marginal probability estimate). This is because, the MLN provides a lifted interpretation, one that generalizes to all possible worlds/instantiations, which are not query/evidence specific. In this paper, we extract grounded-explanations, i.e., explanations defined w.r.t specific inference queries and observed evidence. We extract these explanations from importance weights defined over the MLN formulas that encode the contribution of formulas towards the final inference results. We validate our approach in real world problems related to analyzing reviews from Yelp, and show through user-studies that our explanations are richer than state-of-the-art non-relational explainers such as LIME . 

We report a search for a heavy neutral lepton (HNL) that mixes predominantly with ${\nu }_{\tau }$. The search utilizes data collected with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$collider. The data sample was collected at and just below the center-of-mass energies of the $\mathrm{\Upsilon }\left(4S\right)$and $\mathrm{\Upsilon }\left(5S\right)$resonances and has an integrated luminosity of $915{\mathrm{fb}}^{-1}$, corresponding to $(836\pm 12)\times {10}^6$ $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$events. We search for production of the HNL (denoted $N$) in the decay ${\tau }^{-}\to {\pi }^{-}N$followed by its decay via $N\to {\mu }^{+}{\mu }^{-}{\nu }_{\tau }$. The search focuses on the parameter-space region in which the HNL is long-lived, so that the ${\mu }^{+}{\mu }^{-}$originate from a common vertex that is significantly displaced from the collision point of the KEKB beams. Consistent with the expected background yield, one event is observed in the data sample after application of all the event-selection criteria. We report limits on the mixing parameter of the HNL with the $\tau$neutrino as a function of the HNL mass. Published by the American Physical Society2024 

We measure the branching fraction of the decay $B^{-}\to D^0\rho (770{)}^{-}$using data collected with the Belle II detector. The data contain 387 million $B\overline{B}$pairs produced in $e^{+}{e}^{-}$collisions at the $\mathrm{\Upsilon }\left(4S\right)$resonance. We reconstruct $8360\pm 180$decays from an analysis of the distributions of the $B^{-}$energy and the $\rho (770{)}^{-}$helicity angle. We determine the branching fraction to be $(0.939\pm 0.021\left(\mathrm{stat}\right)\pm 0.050\left(\mathrm{syst}\right))\%$, in agreement with previous results. Our measurement improves the relative precision of the world average by more than a factor of two. Published by the American Physical Society2024 

We search for the rare decay $B^{+}\to K^{+}\nu \overline{\nu }$in a $362{\mathrm{fb}}^{-1}$sample of electron-positron collisions at the $\mathrm{\Upsilon }\left(4S\right)$resonance collected with the Belle II detector at the SuperKEKB collider. We use the inclusive properties of the accompanying $B$meson in $\mathrm{\Upsilon }\left(4S\right)\to B\overline{B}$events to suppress background from other decays of the signal $B$candidate and light-quark pair production. We validate the measurement with an auxiliary analysis based on a conventional hadronic reconstruction of the accompanying $B$meson. For background suppression, we exploit distinct signal features using machine learning methods tuned with simulated data. The signal-reconstruction efficiency and background suppression are validated through various control channels. The branching fraction is extracted in a maximum likelihood fit. Our inclusive and hadronic analyses yield consistent results for the $B^{+}\to K^{+}\nu \overline{\nu }$branching fraction of $[2.7\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst}\left)\right]\times {10}^{-5}$and $\left[{1.1}_{-0.8}^{+0.9}\right(\mathrm{stat}{)}_{-0.5}^{+0.8}\left(\mathrm{syst}\right)]\times {10}^{-5}$, respectively. Combining the results, we determine the branching fraction of the decay $B^{+}\to K^{+}\nu \overline{\nu }$to be $[2.3\pm 0.5(\mathrm{stat}{)}_{-0.4}^{+0.5}\left(\mathrm{syst}\right)]\times {10}^{-5}$, providing the first evidence for this decay at 3.5 standard deviations. The combined result is 2.7 standard deviations above the standard model expectation. Published by the American Physical Society2024 

We report a measurement of decay-time-dependent charge-parity ( $CP$) asymmetries in $B^0\to K_S^0{K}_S^0{K}_S^0$decays. We use $387\times {10}^6$ $B\overline{B}$pairs collected at the $\mathrm{\Upsilon }\left(4S\right)$resonance with the Belle II detector at the SuperKEKB asymmetric-energy electron-positron collider. We reconstruct 220 signal events and extract the $CP$-violating parameters $S$and $C$from a fit to the distribution of the decay-time difference between the two $B$mesons. The resulting confidence region is consistent with previous measurements in $B^0\to K_S^0{K}_S^0{K}_S^0$and $B^0\to \left(c\overline{c}\right)K^0$decays and with predictions based on the standard model. Published by the American Physical Society2024 

A<sc>bstract</sc> We report results from a study ofB^±→ DK^±decays followed byDdecaying to theCP-even final stateK⁺K⁻and CP-odd final state$$ {K}_S^0{\pi}^0 $$ $K_S^0{\pi }^0$, whereDis an admixture ofD⁰and$$ {\overline{D}}^0 $$ ${\overline{D}}^0$states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angleϕ₃. The results are based on a combined analysis of the final data set of 772×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle experiment and a data set of 198×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be$$ \mathcal{A} $$ $A$_CP+= (+12.5±5.8±1.4)% and$$ \mathcal{A} $$ $A$_CP−= (−16.7±5.7±0.6)%, and the ratios of branching fractions to be$$ \mathcal{R} $$ $R$_CP+= 1.164±0.081±0.036 and$$ \mathcal{R} $$ $R$_CP−= 1.151±0.074±0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries$$ \mathcal{A} $$ $A$_CP+and$$ \mathcal{A} $$ $A$_CP−have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^°<ϕ₃< 16.5^°) or (84.5^°<ϕ₃< 95.5^°) or (163.3^°<ϕ₃< 171.5^°) and 0.321 <r_B< 0.465.