Ranked Sparse Signal Support Detection
... achieves asymptotic reliable detection of the support. As before, the equivalence of the two expressions in (13) is due to (8). Comparing the sufficient condition (13) for thresholding with the necessary condition (11), we see two distinct problems with ...
... achieves asymptotic reliable detection of the support. As before, the equivalence of the two expressions in (13) is due to (8). Comparing the sufficient condition (13) for thresholding with the necessary condition (11), we see two distinct problems with ...
Essential Outcomes Seventh Grade Student Progressions
... I can demonstrate p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. (CCSS: 7.NS.1b) ...
... I can demonstrate p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. (CCSS: 7.NS.1b) ...
Web-Scale Information Extraction in KnowItAll
... Etzioni [10] introduced the metaphor of an Information Food Chain where search engines are herbivores “grazing” on the web and intelligent agents are information carnivores that consume output from various herbivores. In terms of this metaphor, the K NOWI TA LL system is an information carnivore tha ...
... Etzioni [10] introduced the metaphor of an Information Food Chain where search engines are herbivores “grazing” on the web and intelligent agents are information carnivores that consume output from various herbivores. In terms of this metaphor, the K NOWI TA LL system is an information carnivore tha ...
Near-ideal model selection by l1 minimization
... to a completely general case. The basic question we would like to address here is how well can one estimate the response Xβ when β happens to have only S nonzero components? From now on, we call such vectors S-sparse. First and foremost, we would like to emphasize that in this paper, we are interest ...
... to a completely general case. The basic question we would like to address here is how well can one estimate the response Xβ when β happens to have only S nonzero components? From now on, we call such vectors S-sparse. First and foremost, we would like to emphasize that in this paper, we are interest ...
Chapter 5 Elements of Probability Theory
... The purpose of this chapter is to summarize some important concepts and results in probability theory. Of particular interest to us are the limit theorems which are powerful tools to analyze the convergence behaviors of econometric estimators and test statistics. These properties are the core of the ...
... The purpose of this chapter is to summarize some important concepts and results in probability theory. Of particular interest to us are the limit theorems which are powerful tools to analyze the convergence behaviors of econometric estimators and test statistics. These properties are the core of the ...
(pdf)
... Maucourant for random walks on hyperbolic groups which are not virtually free [5]. This paper attempts to serve as an introduction to the most important ideas involved in their answer. Section 2 defines hyperbolic groups by a thin-triangles property in their Cayley graphs. Random walks on general gr ...
... Maucourant for random walks on hyperbolic groups which are not virtually free [5]. This paper attempts to serve as an introduction to the most important ideas involved in their answer. Section 2 defines hyperbolic groups by a thin-triangles property in their Cayley graphs. Random walks on general gr ...
pdf
... Clearly Charlie learns something from seeing 100 (or even one) coin toss land heads. This has traditionally been modeled in terms of evidence: the more times Charlie sees heads, the more evidence he has for the coin being heads. There have been a number of ways of modeling evidence in the literatur ...
... Clearly Charlie learns something from seeing 100 (or even one) coin toss land heads. This has traditionally been modeled in terms of evidence: the more times Charlie sees heads, the more evidence he has for the coin being heads. There have been a number of ways of modeling evidence in the literatur ...
A Poisoned Dart for Conditionals
... random variable that takes value 1 at worlds where p and q are both true, 0 at worlds where p is true and q false, and P(q | p) at worlds where p is false. So thinking of C as such a random variable, it takes the value 1 at ½, 0 throughout (1/2, 1], and P(1/2 | [1/2, 1]) = 0 throughout [0, ½). Its o ...
... random variable that takes value 1 at worlds where p and q are both true, 0 at worlds where p is true and q false, and P(q | p) at worlds where p is false. So thinking of C as such a random variable, it takes the value 1 at ½, 0 throughout (1/2, 1], and P(1/2 | [1/2, 1]) = 0 throughout [0, ½). Its o ...
APPROXIMATING THE MINIMUM SPANNING TREE WEIGHT IN SUBLINEAR TIME
... As before, if we know d, then the running time can be made deterministic by stopping execution of the algorithm after Cdwε−2 log dw ε steps for some appropriately chosen constant C. 3.3. Nonintegral weights. Suppose the weights of G are all in the range [1, w], but are not necessarily integral. To e ...
... As before, if we know d, then the running time can be made deterministic by stopping execution of the algorithm after Cdwε−2 log dw ε steps for some appropriately chosen constant C. 3.3. Nonintegral weights. Suppose the weights of G are all in the range [1, w], but are not necessarily integral. To e ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.