Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Enhanced clinical pharmacy service targeting tools: risk-predictive algorithms

Rationale, aims and objectives: This study aimed to determine the value of using a mix of clinical pharmacy data and routine hospital admission spell data in the development of predictive algorithms. Exploration of risk factors in hospitalized patients, together with the targeting strategies devised, will enable the prioritization of clinical pharmacy services to optimize patient outcomes. 

Methods: Predictive algorithms were developed using a number of detailed steps using a 75% sample of integrated medicines management (IMM) patients, and validated using the remaining 25%. IMM patients receive targeted clinical pharmacy input throughout their hospital stay. The algorithms were applied to the validation sample, and predicted risk probability was generated for each patient from the coefficients. Risk threshold for the algorithms were determined by identifying the cut-off points of risk scores at which the algorithm would have the highest discriminative performance. Clinical pharmacy staffing levels were obtained from the pharmacy department staffing database. 

Results: Numbers of previous emergency admissions and admission medicines together with age-adjusted co-morbidity and diuretic receipt formed a 12-month post-discharge and/or readmission risk algorithm. Age-adjusted co-morbidity proved to be the best index to predict mortality. Increased numbers of clinical pharmacy staff at ward level was correlated with a reduction in risk-adjusted mortality index (RAMI). 

Conclusions: Algorithms created were valid in predicting risk of in-hospital and post-discharge mortality and risk of hospital readmission 3, 6 and 12 months post-discharge. The provision of ward-based clinical pharmacy services is a key component to reducing RAMI and enabling the full benefits of pharmacy input to patient care to be realized.

Efficient Algorithms for Answering the m-Closest Keywords Query

As an important type of spatial keyword query, the m-closest keywords (mCK) query finds a group of objects such that they cover all query keywords and have the smallest diameter, which is defined as the largest distance between any pair of objects in the group. The query is useful in many applications such as detecting locations of web resources. However, the existing work does not study the intractability of this problem and only provides exact algorithms, which are computationally expensive.

In this paper, we prove that the problem of answering mCK queries is NP-hard. We first devise a greedy algorithm that has an approximation ratio of 2. Then, we observe that an mCK query can be approximately answered by finding the circle with the smallest diameter that encloses a group of objects together covering all query keywords. We prove that the group enclosed in the circle can answer the mCK query with an approximation ratio of 2 over 3. Based on this, we develop an algorithm for finding such a circle exactly, which has a high time complexity. To improve efficiency, we propose another two algorithms that find such a circle approximately, with a ratio of 2 over √3 + ε. Finally, we propose an exact algorithm that utilizes the group found by the 2 over √3 + ε)-approximation algorithm to obtain the optimal group. We conduct extensive experiments using real-life datasets. The experimental results offer insights into both efficiency and accuracy of the proposed approximation algorithms, and the results also demonstrate that our exact algorithm outperforms the best known algorithm by an order of magnitude.