Huber loss

In statistics, the Huber loss is a loss function used in robust regression, less sensitive to outliers in data than the squared error loss. A variant for classification is sometimes used; the Huber loss function describes the penalty incurred by an estimation procedure f. Huber defines the loss function piecewise by L δ = { 1 2 a 2 for | a | ≤ δ, δ, otherwise; this function is quadratic for small values of a, linear for large values, with equal values and slopes of the different sections at the two points where | a | = δ. The variable a refers to the residuals, to the difference between the observed and predicted values a = y − f, so the former can be expanded to L δ = { 1 2 2 for | y − f | ≤ δ, δ | y − f | − 1 2 δ 2 otherwise. Two commonly used loss functions are the squared loss, L = a 2, the absolute loss, L = | a |; the squared loss function results in an arithmetic mean-unbiased estimator, the absolute-value loss function results in a median-unbiased estimator. The squared loss has the disadvantage that it has the tendency to be dominated by outliers—when summing over a set of a's, the sample mean is influenced too much by a few large a -values when the distribution is heavy tailed: in terms of estimation theory, the asymptotic relative efficiency of the mean is poor for heavy-tailed distributions.

As defined above, the Huber loss function is convex in a uniform neighborhood of its minimum a = 0. These properties allow it to combine much of the sensitivity of the mean-unbiased, minimum-variance estimator of the mean and the robustness of the median-unbiased estimator; the Pseudo-Huber loss function can be used as a smooth approximation of the Huber loss function. It combines the best properties of L2 squared loss and L1 absolute loss by being convex when close to the target/minimum and less steep for extreme values; this steepness can be controlled by the δ value. The Pseudo-Huber loss function ensures, it is defined as L δ = δ 2. As such, this function approximates a 2 / 2 for small values of a, approximates a straight line with slope δ for large values of a. While the above is the most common form, other smooth approximations of the Huber loss function exist. For classification purposes, a variant of the Huber loss called. Given a predic

James Alfred Davidson

James Alfred Davidson, OBE, was a British naval commander and diplomat. During the Second World War James Davidson served in every theatre of the war at sea; when peace came, he joined the Commonwealth Relations Office, after working in Cambodia as the Khmer Rouge took over, he held high posts in Brunei and the British Virgin Islands. Turning to the law after his retirement from the Diplomatic Service, he had a third career with the Pensions appeal tribunal. Davidson was born in 1921 and educated at Portsmouth Grammar School and Christ's Hospital at the Royal Naval College, Dartmouth, his first posting, as a midshipman, was to the old cruiser HMS Hawkins, but in 1942 he was transferred to the destroyer HMS Inconstant, with which he took part in the first successful British landing of the war, at Diego Suarez in Madagascar. In 1943 he was appointed first lieutenant of the frigate HMS Calder. On escort and anti-submarine duties in the Western Approaches and the Mediterranean, the Calder was credited with sinking three U-boats, never lost a ship on the fast troop convoys to Malta.

In February 1944 Davidson took temporary command of the ship aged just 21. Shortly after D-Day, Davidson joined HMS Rocket, an Eastern Fleet destroyer which took part in the Battle of Penang. After postwar pilot training, he served as executive officer and first lieutenant on HMS Childers, which took part in the painful and sensitive operation of policing illegal Jewish immigration into Palestine. In 1951 he was posted as naval liaison officer to the Chinese Nationalist Government; the post was a sensitive one, with the Korean War in progress and the Communist Chinese threatening the offshore islands. The nationalist leader Chiang Kai-shek lived close by and Davidson was invited to the family home to play mah-jong. On his return to England, Davidson was promoted and became commanding officer of the minesweeper HMS Welfare, on minesweeping and fishery protection duties, but he found the peacetime Navy less attractive than wartime service and decided to seek an alternative career. He married his wife Daphne While in 1955.

After being called to the Bar, he joined the Commonwealth Relations Office in 1960. His first assignment was as first secretary in the newly independent Trinidad. In 1969, though, he was posted to Phnom Penh, where he formed a good relationship with the head of state, Prince Sihanouk. In 1970 Sihanouk was deposed in a military coup; the British and American embassies were the only ones to keep families on in Cambodia, the Davidsons were kept awake at night by the mortar fire of the Khmer Rouge closing in on the city. All those who worked for them fell victim to the horrors of "Year Zero". Davidson was an acknowledged authority on the region and his book, Indo-China: Signposts in the Storm was well received. In 1972 Davidson, appointed OBE the previous year, was asked to go to East Pakistan as deputy high commissioner; the India-Pakistan war had just concluded and his first task was to witness mass burials of the victims. He worked with Sheikh Mujibur Rahman, the first Prime Minister of the new state of Bangladesh, he was involved in the negotiations which took place on Indira Gandhi's visit to the new country in March 1972.

The disaster of Bangladesh had attracted much Western aid and, with it, the interest of those looking for a quick profit. Davidson's visitors in Dhaka in the early days included Robert Maxwell. Davidson ejected the former from his residence and politely refused the latter's forceful demands that aid money be spent on Pergamon Press publications rather than bailey bridges, he ignored Maxwell's threats of dire consequences from "powerful friends" back in London. After Bangladesh, Davidson had two appointments as head of mission; the first was in Brunei where, as High Commissioner, he was accommodated in Somerset Maugham's old house. He became a trusted adviser to the Brunei Royal Family during the delicate negotiations towards the new treaty of friendship and independence, his final posting was as Governor of the British Virgin Islands. While there, he gained the trust of the population, hostile to the idea of a British Governor after the recent constitutional negotiations, he resisted early attempts by organised crime to infiltrate the colony's financial institutions.

He retired from the Diplomatic Service in 1981. After a period as a visiting fellow at the London School of Economics he decided to do a pupillage at the Admiralty Bar, his knowledge of minesweeping and wartime ship design proved unexpectedly helpful during the inquiry into the sinking of the European Gateway. But it was not practical for him to embark on a career at the Bar at the age of 60, in 1982 he accepted appointments as legal chairman of Mental Health Review Tribunals and deputy president of the Pensions appeal tribunal, jobs which occupied him full-time for the next 13 years. In the mid-1990s he acted as the president of the Pensions Appeal Tribunal, but he declined an invitation to do the job permanently

Dwight Hemion

Dwight Arlington Hemion Jr. was an American television director known for music-themed television programs of the 1960s and 1970s. He held the record for the most Emmy nominations, won 18 times, putting him at the top of his profession throughout the 1960s, 1970s, well into the 1980s, he won the Directors Guild of America's top TV award five times, six Ace awards and a Peabody award. Hemion began working in live television in New York City in the 1950s for the original The Tonight Show starring Steve Allen. In the 1960s, Hemion began concentrating on musical-variety shows, working with producer Gary Smith on a popular series of Kraft Music Hall specials for NBC-TV. Smith-Hemion Productions arguably defined the fast-paced look and glamorous style of the American comedy-variety genre, influenced scores of generations working in television. Hemion had a knack for balancing both visual and musical elements that made him a master of directing concert performance specials, he worked with such major stars as Frank Sinatra, Bing Crosby, Barbra Streisand, Paul McCartney, Bette Midler, Shirley MacLaine, Julie Andrews, Elvis Presley, Burt Bacharach, The Muppets, Luciano Pavarotti.

He won Emmys for directing the Kennedy Center Honors in 1989 and 1990. Among the most memorable specials that Hemion produced and directed were: My Name Is Barbra, Frank Sinatra: A Man and His Music, Peter Pan, Baryshnikov on Broadway, Barbra Streisand: The Concert. Along with producing partner Gary Smith, Hemion branched out into producing large conventions, including the nomination conventions for the Democratic Party as well as the inaugural ceremonies for Ronald Reagan and Bill Clinton.. He is credited as a Executive Producer for The Star Wars Holiday Special along with Smith Hemion died of kidney failure in Rectortown, Virginia, at the age of 81. Dwight Hemion on IMDb Dwight Hemion at The Interviews: An Oral History of Television Dwight Hemion at Find a Grave