We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our method, nuclear penalized multinomial regression (NPMR), to Major League Baseball play-by-play data to predict outcome probabilities based on batter-pitcher matchups. The interpretation of the results meshes well with subject-area expertise and also suggests a novel understanding of what differentiates players.
The RFID cards contain chips, that combined with readers in the poker table, transmit information about each player’s hole cards, so that viewers can see the cards on the broadcast (which is on a 30-minute delay to protect game integrity).
As he spoke about the heightened risk, the NASA administrator also emphasized that both the space station and the astronauts aboard it are safe. The station can be maneuvered out of harm’s way if needed, he added.
But another danger, he said, is that “when one country does it, then other countries feel like they have to do it, as well.”
Before committing any real money, the researchers tested the idea on 10 years of historical data on the closing odds and results of 479,440 soccer games played between 2005 and 2015. This simulation paid out 44 percent of the time and delivered a yield of 3.5 percent over the 10-year period. “For an imaginary stake of $50 per bet, this corresponds to an equivalent profit of $98,865 across 56,435 bets,” they say.
“Beating humans isn’t really our goal; it’s just a milestone along the way,” Sandholm said. “What we want to do is create an artificial intelligence that can help humans negotiate or make decisions in situations where they can’t know all of the facts.”
“The advances made in Claudico over Tartanian7 in just eight months were huge,” Les said, a rate of improvement that suggests the AI might need only another year before it clearly plays better than the pros.
Poker being what it is, the robot, named Cepheus after a constellation in the northern hemisphere, will lose if it’s dealt an inferior hand, but it will minimize its losses as best as is mathematically possible and will slowly but surely take your money by making the “perfect” decision in any given scenario. Heads-up limit Hold’Em, it can be said, has been “solved.”
And it was solved by computer scientists at the University of Alberta who don’t actually play the game. That’s because solving the game is more of a math problem than anything else.
This development is like when they discovered Basic Strategy for blackjack.
After losing with a rock, for example, a player was more likely to play paper in the next round than the “one in three” rule would predict.
This “win-stay lose-shift” strategy is known in game theory as a conditional response – and it may be hard-wired into the human brain, the researchers say
So let’s look at the probability that none of the 23 people in the room share the same birthday. For two people, the probability that the second person doesn’t have the same birthday as the first is 364/365. Then the probability that those two are different and that a third doesn’t share the same birthday as either of them is 364/365 × 363/365. Likewise, the probability that those three have different birthdays and that the fourth does not share the same birthday as any of those first three is 364/365 × 363/365 × 362/365. Continuing like this, the probability that none of the 23 people share the same birthday is 364/365 × 363/365 × 362/365 × 361/365 … × 343/365.
This equals 0.49