ICU mortality scoring systems attempt to predict patient mortality using predictive models with various clinical predictors. Examples of such systems are APACHE, SAPS and MPM. However, most such scoring systems do not actively look for and include interaction terms, despite physicians intuitively taking such interactions into account when making a diagnosis. One barrier to including such terms in predictive models is the difficulty of using most variable selection methods in high-dimensional datasets. A genetic algorithm framework for variable selection with logistic regression models is used to search for two-way interaction terms in a clinical dataset of adult ICU patients, with separate models being built for each category of diagnosis upon admittance to the ICU. The models had good discrimination across all categories, with a weighted average AUC of 0.84 (>0.90 for several categories) and the genetic algorithm was able to find several significant interaction terms, which may be able to provide greater insight into mortality prediction for health practitioners. The GA selected models had improved performance against stepwise selection and random forest models, and provides greater flexibility in terms of variable selection by being able to optimize over any modeler-defined model performance metric instead of a specific variable importance metric.

Genetic algorithms are a well-known method for tackling the problem of variable selection. As they are non-parametric and can use a large variety of fitness functions, they are well-suited as a variable selection wrapper that can be applied to many different models. In almost all cases, the chromosome formulation used in these genetic algorithms consists of a binary vector of length n for n potential variables indicating the presence or absence of the corresponding variables. While the aforementioned chromosome formulation has exhibited good performance for relatively small n, there are potential problems when the size of n grows very large, especially when interaction terms are considered. We introduce a modification to the standard chromosome formulation that allows for better scalability and model sparsity when interaction terms are included in the predictor search space. Experimental results show that the indexed chromosome formulation demonstrates improved computational efficiency and sparsity on high-dimensional datasets with interaction terms compared to the standard chromosome formulation.

In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete applications such as dictionary learning, generalized phase retrieval, and orthogonal tensor decomposition are known to induce such structures. We describe a second-order trust-region algorithm that provably converges to a global minimizer efficiently, without special initializations. Finally we highlight alternatives, and open problems in this direction.

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a distance-based iterative method for clustering data in very high-dimensional space, using the $\ell_1$-metric that is less sensitive to high dimensionality than the Euclidean distance. For $K$ clusters in $\mathbb{R}^n$, the problem decomposes to $K$ problems coupled by probabilities, and an iteration reduces to finding $Kn$ weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

Google's parent company Alphabet saw its revenue grow 17% during the first three months of this year, the company said on Thursday, but spent more money on its experimental moonshot projects, engineers, data centers and YouTube shows, causing it to miss investors' profit expectations. Alphabet shares dropped more than 4% in the US during after-hours trading to about 724 a share. The dilemma illustrates Alphabet's key challenge as it seeks to become the technology firm most omnipresent in consumers lives, including search, email, smartphones, maps, self-driving cars, virtual reality and even cancer research. Alphabet's growth has also attracted attention from regulators. On 20 April, the European Union's antitrust regulators charged the company with using its mobile operating system, Android, to block out competitors.

SAN FRANCISCO -- The cloud may be the future, but the specter of the PC lingers. Microsoft is the latest tech giant whose earnings say that loud and clear. Microsoft on Thursday posted substantial drops in revenue and earnings as it continues to navigate from its legacy PC business into emerging technologies -- a day after chipmaker Intel announced a 11% workforce reduction. The Redmond, Wash.-based company reported a 6% decline in fiscal third-quarter revenue to 20.5 billion. Earnings of 3.8 billion, or 47 cents per share, fell 25%in the same quarter a year ago.

SAN FRANCISCO -- Google parent Alphabet reported first-quarter earnings that fell short of analyst expectations as growing losses from the tech giant's investments in speculative businesses, from self-driving cars to speedy Internet access, overshadowed Google's booming advertising business. Class A shares of Alphabet (GOOGL) fell 6% after hours to 732. They've rallied 44% in the past 12 months. "Alphabet has made it pretty clear they weren't going to stop their investments in other areas, and they spent a little bit more than some people may have liked," said BGC Financial analyst Colin Gillis. "You don't necessarily like to see costs and losses growing faster than revenue, but that's where Alphabet's future is going to be." Chief Financial Officer Ruth Porat, who joined the company last May in a hire investors hoped would curb spending, assured investors that Alphabet is "thoughtfully pursuing big bets."

Every decade or so, a new era of computing comes along that shapes everything we do. Much of the 90s was about client-server and Windows PCs. By the aughts, the Web had taken over and every advertisement carried a URL. Then came the iPhone, and we're in the midst of a decade defined by people tapping myopically into tiny screens. So what comes next, when mobile gives way to something else?

SAN FRANCISCO -- The cloud may be the future, but the specter of the PC lingers. Microsoft is the latest tech giant to learn that first-hand. Microsoft on Thursday posted substantial drops in revenue and earnings as it continues to navigate from its legacy PC business into emerging technologies -- a day after chip maker Intel announced a 11% workforce reduction. The computing giant reported a 5% decline in fiscal third-quarter revenue to 20.5 billion. Earnings of 3.8 billion, or 47 cents per share, fell from 5 billion, or 61 cents a share, in the same quarter a year ago.

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