Abstract: In the context of power-system decarbonization and the rising share of distributed renewables, risk assessment for distribution networks faces two coupled difficulties: probabilistic power-flow models are expensive for online use, and high-dimensional uncertainties inflate surrogate models with numerous irrelevant terms. This paper proposes a distribution-network risk-assessment approach that combines sparse polynomial chaos expansion (PCE) with Least Absolute Shrinkage and Selection Operator (Lasso) regression to obtain a compact surrogate for probabilistic power flow and subsequent risk quantification. This method replaces the nonlinear power-flow solver in stochastic simulations with a data-driven PCE surrogate that maps uncertain inputs, such as renewable generation, load levels, and equipment parameters, to nodal voltages and branch flows. A two-stage sparsification strategy is used to control the model size while preserving fidelity. First, term-level sensitivities computed from the estimated PCE coefficients prune polynomials that contribute negligibly to the response; therefore, dominant first-order effects and essential second-order interactions are retained, while redundant bases are removed. Second, Lasso regression ranks and selects the remaining variables and basis functions by contribution magnitude, yielding an interpretable expansion with reduced variance and improved numerical stability. Input correlations among random variables are modeled via the Nataf transformation; therefore, training and evaluation are performed under a realistic joint distribution rather than an independence assumption. Based on the surrogate outputs, static security risk indices are constructed for distribution networks. The indices quantify the voltage-limit and branch-flow-limit risks by combining two elements: the probability of limit violation and associated severity on the physical magnitude scale. Node- and branch-level indices are first computed and then aggregated into system-level indicators through a consistent summation scheme to reflect the overall risk of the operating point while maintaining a clear physical interpretation. This construction supports comparison across scenarios and operating conditions without introducing ad hoc weighting. The methodology was validated on three systems: the IEEE 33-node and IEEE 118-node benchmarks and a large-scale 322-node comprehensive distribution network. For each system, uncertain inputs were characterized by empirical distributions and cross-correlations, and training and validation samples were generated accordingly and used to fit and evaluate the sparse PCE surrogate. The results show that the surrogate reproduced the distributions of nodal voltages and branch flows obtained by conventional probabilistic power flow while requiring only a small subset of candidate polynomial bases. The two-stage sparsification substantially reduced the number of retained terms compared to dense PCE constructions, which lowers the training cost and accelerates the evaluation for risk analysis. The risk indices computed from the surrogate closely tracked those from full stochastic simulations across nodes and branches, and the system-level indicators preserved the same trends under variations in renewable output, load level, and correlation strength. This method remained stable as the network size increased from tens to several hundred nodes, supporting its applicability in realistic studies. In summary, the Lasso-based sparse PCE framework provides a compact surrogate for probabilistic power flow and a coherent set of static security risk indices for distribution networks with high renewable penetration. By combining term-level sensitivity pruning, Lasso-based selection, and correlation modeling through the Nataf transformation, this approach preserves essential physics while alleviating the dimensionality burden. Case studies on IEEE 33, IEEE 118, and a 322-node network indicate that the method maintains assessment accuracy and significantly improves computational efficiency, thereby enabling online or near-real-time risk evaluation and operation-oriented decision support.