This paper considers the expected penalty functions for a discrete semi-Markov risk model with randomized dividends. Under the model, individual claims are governed by a Markov chain with finite state space, and the insurer pays a dividend of 1 with a probability at the end of each period if the present surplus is greater than or equal to a threshold value. Recursive formulae and the initial va...

Decision trees effectively represent the sparse, high dimensional and noisy nature of chemical data from experiments. Having learned a function from this data, we may want to thereafter optimize the function, e.g., picking the best chemical process catalyst. In this way, we may repurpose legacy predictive models. This work studies a large-scale, industrially-relevant mixed-integer quadratic opt...

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are...

When applying independent component analysis (ICA), sometimes we expect that the connections between the observed mixtures and the recovered independent components (or the original sources) to be sparse, to make the interpretation easier or to reduce the model complexity. In this paper we propose natural gradient algorithms for ICA with a sparse separation matrix, as well as ICA with a sparse m...

The transformed l1 penalty (TL1) functions are a one parameter family of bilinear transformations composed with the absolute value function. When acting on vectors, the TL1 penalty interpolates l0 and l1 similar to lp norm (p ∈ (0, 1)). In our companion paper, we showed that TL1 is a robust sparsity promoting penalty in compressed sensing (CS) problems for a broad range of incoherent and cohere...

For a general class of risk models, the dividends-penalty identity is derived by probabilistic reasoning. This identity is the key for understanding and determining the optimal dividend barrier, which maximizes the difference between the expected present value of all dividends until ruin and the expected discounted value of a penalty at ruin (which is typically a function of the deficit at ruin...

The P-splines of Eilers andMarx (Stat Sci 11:89– 121, 1996) combine aB-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as reduced rank smoothers: (i) the basis and the penalty are sparse, enabling efficient computation, especially for Bayesian stochastic simulati...

We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function (PLPF) and an `2-penalty function. The PLPF is defined by a set of penalty parameters that correspond to break points of the PLPF and are updated at every iteration. The `2-penalty function, like traditional penalty functions for NLP, is defined b...

This paper studies the sparsistency, rates of convergence, and asymptotic normality for estimating sparse covariance matrices based on penalized likelihood with non-concave penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur ...