Naive Feature Selection: Sparsity in Naive Bayes

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact solution in the case of binary data, or a bound in the multinomial case. We prove that our bound becomes tight as the marginal contribution of additional features decreases. Both binary and multinomial sparse models are solvable in time almost linear in problem size, representing a very small extra relative cost compared to the classical naive Bayes. Numerical experiments on text data show that the naive Bayes feature selection method is as statistically effective as state-of-the-art feature selection methods such as recursive feature elimination, $l_1$-penalized logistic regression and LASSO, while being orders of magnitude faster. For a large data set, having more than with $1.6$ million training points and about $12$ million features, and with a non-optimized CPU implementation, our sparse naive Bayes model can be trained in less than 15 seconds

Thermomechanical and hygroelastic properties of an epoxy system under humid and cold-warm cycling conditions

In this paper, we study the hygrothermal aging of an anhydride-cured epoxy under temperature and hygrometry conditions simulating those experienced by an aircraft in wet tropical or subtropical regions. Gravimetric and dimensional measurements were performed and they indicate that there are three stages in this aging process: the first one, corresponding to the early cycles can be called the “induction stage”. The second stage of about 1000 cycles duration, could be named the “swelling stage”, during which the volume increase is almost equal to the volume of the (liquid) water absorbed. Both the first and second stages are accompanied by modifications of the mechanical properties and the glass transition temperature. During the third (“equilibrium”) stage, up to 3000 cycles, there is no significant change in the physical properties despite the continuous increase of water uptake. This can be explained by the fact that only physically sorbed water can influence physical properties

Approximation Bounds for Sparse Programs

We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization procedure to recover feasible points satisfying these bounds. These error bounds are proportional to the rate of growth of the objective with the target cardinality, which means in particular that the relaxation is nearly tight as soon as the target cardinality is large enough so that only uninformative features are added

Acute myopathy secondary to oral steroid therapy in a 49-year-old man: a case report

<p>Abstract</p> <p>Introduction</p> <p>Acute myopathy caused by oral corticosteroids is rare. We present a case of myopathy occurring after two doses of methylprednisolone. Typically, acute steroid myopathy occurs with therapy using intravenous corticosteroids at high doses. Acute myopathy developing very early in the course of treatment with oral corticosteroids has been reported only once in the literature. Corticosteroid therapy may be complicated by myopathy, usually chronic, after prolonged high-dose therapy. Acute myopathy caused by exogenous corticosteroids is rare, usually with intravenous corticosteroids at high doses.</p> <p>Case presentation</p> <p>A 49-year-old Caucasian man developed acute myopathy after taking oral methylprednisolone for only two days, 24 mg on day 1 and 20 mg on day 2. He discontinued the medication because of new-onset myalgias and lethargy on day 3 and was seen in our clinic four days after beginning therapy. He completely recovered in four weeks by discontinuing the corticosteroids.</p> <p>Conclusion</p> <p>Among the many complications of corticosteroid therapy, acute myopathy is very rare. It requires prompt recognition and adjustment of therapy.</p