NEW YORK—Neiman Marcus is hoping to capitalize on rebounding luxury sales by investing more than $500 million over the next three years in refreshing stores, speeding up deliveries and acquiring new technology. The plan, unveiled Tuesday, includes a pact to purchase Stylyze Inc., a tech startup that recommends outfits for customers based on past purchases and browsing history. Neiman Marcus has been working with the company since 2018 and decided to buy it outright because of its potential, according to the luxury retailer’s CEO, Geoffroy van Raemdonck. He says the machine learning technology has helped convert online browsers into buyers and enticed shoppers to keep coming back. Financial terms were not disclosed. Neiman Marcus emerged from Chapter 11 bankruptcy protection last September, one of the most high-profile retail bankruptcies at the onset of the pandemic. Like many of its peers, the privately held department store chain was forced to temporarily …