Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting outliers in HMM data series

Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality. We show that some of these conditions are equivalent to the existence of an appropriate notion of a Weierstrass model adapted to the toric context. Moreover, we show that if in addition other conditions are satisfied, there exists a toric semistable degeneration of the elliptic K3 surface which is compatible with the elliptic fibration and F-theory/Heterotic duality.Comment: References adde

Faster Query Answering in Probabilistic Databases using Read-Once Functions

A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can be computed in polynomial time (whereas the general problem for arbitrary expressions is #P-complete). Known approaches to checking read-once property seem to require putting these expressions in disjunctive normal form. In this paper, we tell a better story for a large subclass of boolean event expressions: those that are generated by conjunctive queries without self-joins and on tuple-independent probabilistic databases. We first show that given a tuple-independent representation and the provenance graph of an SPJ query plan without self-joins, we can, without using the DNF of a result event expression, efficiently compute its co-occurrence graph. From this, the read-once form can already, if it exists, be computed efficiently using existing techniques. Our second and key contribution is a complete, efficient, and simple to implement algorithm for computing the read-once forms (whenever they exist) directly, using a new concept, that of co-table graph, which can be significantly smaller than the co-occurrence graph.Comment: Accepted in ICDT 201

Faster query answering in probalistic databases using read-once functions

A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can be computed in polynomial time (whereas the general problem for arbitrary expressions is #P-complete). Known approaches to checking read-once property seem to require putting these expressions in disjunctive normal form. In this paper, we tell a better story for a large subclass of boolean event expressions: those that are generated by conjunctive queries without self-joins and on tuple-independent probabilistic databases. We first show that given a tuple-independent representation and the provenance graph of an SPJ query plan without self-joins, we can, without using the DNF of a result event expression, efficiently compute its co-occurrence graph. From this, the read-once form can already, if it exists, be computed efficiently using existing techniques. Our second and key contribution is a complete, efficient, and simple to implement algorithm for computing the read-once forms (whenever they exist) directly, using a new concept, that of co-table graph, which can be significantly smaller than the cooccurrence graph

A Comprehensive Framework for Evaluating Time to Event Predictions using the Restricted Mean Survival Time

The restricted mean survival time (RMST) is a widely used quantity in survival analysis due to its straightforward interpretation. For instance, predicting the time to event based on patient attributes is of great interest when analyzing medical data. In this paper, we propose a novel framework for evaluating RMST estimations. Our criterion estimates the mean squared error of an RMST estimator using Inverse Probability Censoring Weighting (IPCW). A model-agnostic conformal algorithm adapted to right-censored data is also introduced to compute prediction intervals and to evaluate variable importance. Our framework is valid for any RMST estimator that is asymptotically convergent and works under model misspecification