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Statistical and Computational Guarantees for the Baum-Welch Algorithm
The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its observation process is often addressed via the Baum-Welch algorithm, which is known to be susceptible to local optima. In this paper, we first give a general characterization of the basin of attraction associated with any global optimum of the population likelihood. By exploiting this characterization, we provide non-asymptotic finite sample guarantees on the Baum-Welch updates and show geometric convergence to a small ball of radius on the order of the minimax rate around a global optimum. As a concrete example, we prove a linear rate of convergence for a hidden Markov mixture of two isotropic Gaussians given a suitable mean separation and an initialization within a ball of large radius around (one of) the true parameters. To our knowledge, these are the first rigorous local convergence guarantees to global optima for the Baum-Welch algorithm in a setting where the likelihood function is nonconvex. We complement our theoretical results with thorough numerical simulations studying the convergence of the Baum-Welch algorithm and illustrating the accuracy of our predictions.
algorithms  statistics  machine_learning  martin.wainwright 
6 hours ago by rvenkat
Image Dithering: Eleven Algorithms and Source Code
Today’s graphics programming topic – dithering – is one I receive a lot of emails about, which some may find surprising. You might think that dithering is something programmers shouldn’t have to deal with in 2012. Doesn’t dithering belong in the annals of technology history, a relic of times when “16 million color displays” were something programmers and users could only dream of? In an age when cheap mobile phones operate in full 32bpp glory, why am I writing an article about dithering?
dithering  algorithms  graphics 
23 hours ago by amason
javascript-algorithms/ at master · trekhleb/javascript-algorithms
Algorithms and data structures implemented in JavaScript with explanations and links to further readings
javascript  js  programming  algorithms  lists 
yesterday by dionidium
javascript-algorithms/ at master · trekhleb/javascript-algorithms
Algorithms and data structures implemented in JavaScript with explanations and links to further readings
javascript  algorithm  algorithms  example  computer-science  github 
yesterday by grinful
donnemartin/system-design-primer: Learn how to design large-scale systems. Prep for the system design interview. Includes Anki flashcards.
InterviewQ stuff. Nice tutorial/chart on how to design large scale systems. Also lots of algorithms and data structure stuff for interview questions. Also has Anki cards.
programming  Design  System  Servers  backend  Interview  Algorithms  coding  DataStructure  Anki 
yesterday by lost_in_space
Inside FreshDirect’s Big Bet to Win the Home-Delivery Fight - WSJ
By Jennifer Smith
July 18, 2018 5:30 a.m

Designed to keep food fresh longer and move it faster, FreshDirect’s 400,000 square-foot distribution centre is the online grocer’s multimillion-dollar bet on the fastest-growing sector in the grocery business, home-delivery. FreshDirect pioneered the e-commerce home-delivery market, and now with Amazon and big grocery chains like Kroger Co. piling on investments, companies are jockeying for position in a business that some believe is the future of supermarket sales.....FreshDirect's trucks now provide next-day delivery to customers across the New York-New Jersey, Philadelphia and Washington, D.C., metropolitan areas, with plans to expand into Boston next. The private company says it generated between $600 million and $700 million in annual revenue in 2017.

It declined to disclose the cost of the new facility, which was financed with the help of a $189 million investment round in 2016 led by J.P. Morgan Asset Management, direct funding and incentives from state and local governments......Amazon, Target Corp. and other large companies have invested hundreds of millions of dollars to expand food delivery and build out their grocery e-commerce operations. Supermarket chain owner Koninklijke Ahold Delhaize NV’s Peapod unit, the longest-running online grocery service in the U.S., has expanded to 24 markets and is investing in technology to cut its handling and delivery costs.

Walmart Inc. said this month that, the online retailer it bought two years ago, will open a fulfillment center in the Bronx this fall to help roll out same- and next-day grocery deliveries in New York City.

The grocers are trying to solve one of the toughest problems in home delivery: Getting food to doorsteps in the same condition consumers would expect if they went to the store themselves. Delivering perishables is trickier than dropping off paper towels or dogfood. Fruit bruises, meat spoils, eggs break. ........FreshDirect’s logistic hurdles start well before delivery. It must get products from its suppliers to the building, process the food, then pick, pack and ship orders before the quality degrades.

That is why the new distribution centre has 15 different temperature zones. Tomatoes do best at about 55 degrees, but “chicken and meat like it to be just at 32 degrees... it gives more of shelf life to it,"....Software determines the most efficient route for each order, and tells workers which items to pick.....A big part of the facility [distribution centre] is ripping out tons and tons of operating costs out of the business.....The stakes in getting the technology right are high. FreshDirect is competing with grocery chains that often fill online orders through their stores, using a mix of staff and third-party services like Instacart Inc. So-called click-and-collect services, where consumers swing by to pick up their own orders, tend to have better margins because the retailer isn’t paying for last-mile delivery.....Online-only operations with centralized warehouses tend to be more efficient than logistics run out of stores, because they use fewer workers and can position goods for faster fulfillment.
algorithms  Amazon  big_bets  cold_storage  distribution_centres  distribution  e-commerce  food  FreshDirect  grocery  home-delivery  infrastructure  Kroger  logistics  perishables  retailers  software  supermarkets  Target  Wal-Mart  warehouses  fulfillment  last_mile 
yesterday by jerryking

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