On Talagrand\`s deviation inequalities for product measures
... procedure that yields concentration inequalities of the type (1.2) via a simple dierential inequality on Laplace transforms. This has been shown in Davies and Simon (1984), Aida et al.(1994) and Ledoux (1995) and we recall the simple steps here. In the recent note Bobkov (1995), Talagrand's inequal ...
... procedure that yields concentration inequalities of the type (1.2) via a simple dierential inequality on Laplace transforms. This has been shown in Davies and Simon (1984), Aida et al.(1994) and Ledoux (1995) and we recall the simple steps here. In the recent note Bobkov (1995), Talagrand's inequal ...
Learning Sums of Independent Integer Random Variables
... be the case that at least one of the k − 1 values 1, 2, . . . , k − 1 makes a “large contribution” to Var(S). (This is made precise by working with “0-moded” SIIRVs and analyzing the “b-weight” of the SIIRV for b ∈ {1, . . . , k − 1}; see Definition 2.2 for details.) It is useful to first consider t ...
... be the case that at least one of the k − 1 values 1, 2, . . . , k − 1 makes a “large contribution” to Var(S). (This is made precise by working with “0-moded” SIIRVs and analyzing the “b-weight” of the SIIRV for b ∈ {1, . . . , k − 1}; see Definition 2.2 for details.) It is useful to first consider t ...
On the `Semantics` of Differential Privacy: A Bayesian Formulation
... Given a particular transcript t, we say privacy has been breached if the adversary would draw different conclusions about the world and, in particular, about a person i, depending on whether or not i’s data was used. One could formally define “different” in many ways. In this paper, we choose a weak ...
... Given a particular transcript t, we say privacy has been breached if the adversary would draw different conclusions about the world and, in particular, about a person i, depending on whether or not i’s data was used. One could formally define “different” in many ways. In this paper, we choose a weak ...
The Sample Complexity of Exploration in the Multi
... The focus of this paper is the classical multi-armed bandit problem, but rather than looking at the expected regret, we are concerned with PAC-type bounds on the number of steps needed to identify a near-optimal arm. In particular, we are interested in the expected number of steps that are required ...
... The focus of this paper is the classical multi-armed bandit problem, but rather than looking at the expected regret, we are concerned with PAC-type bounds on the number of steps needed to identify a near-optimal arm. In particular, we are interested in the expected number of steps that are required ...
Reducing belief simpliciter to degrees of belief
... believes A nor ¬A and in this sense suspends judgment on A. One the other hand, by quantitative belief we mean the assignment of numerical degrees of belief to propositions, so that any such degree measures the strength of an agent’s belief in a proposition. Typically, A is believed to degree 1 mean ...
... believes A nor ¬A and in this sense suspends judgment on A. One the other hand, by quantitative belief we mean the assignment of numerical degrees of belief to propositions, so that any such degree measures the strength of an agent’s belief in a proposition. Typically, A is believed to degree 1 mean ...
Bearden and Murphy
... to account for the bias. In a paper on the CSP, Seale and Rapoport (1997) suggested that the bias results from an endogenous search cost: Because search is inherently costly (see, Stigler, 1961), the DM’s payoff increases in the payoff she receives for selecting the best applicant but decreases in t ...
... to account for the bias. In a paper on the CSP, Seale and Rapoport (1997) suggested that the bias results from an endogenous search cost: Because search is inherently costly (see, Stigler, 1961), the DM’s payoff increases in the payoff she receives for selecting the best applicant but decreases in t ...
Benchmarking real-valued acts
... they meet a given target. See Bordley (2002). The benchmarking procedure is more general than it may appear: we show in Section 3.2 that it includes expected utility as a special case. Of course, one can apply the existing axiomatizations for preference representation to the benchmarking procedure s ...
... they meet a given target. See Bordley (2002). The benchmarking procedure is more general than it may appear: we show in Section 3.2 that it includes expected utility as a special case. Of course, one can apply the existing axiomatizations for preference representation to the benchmarking procedure s ...
The degree sequence of a scale
... most basic properties of a graph or network is its degree sequence. For the standard random graph model n m of all graphs with m edges on a fixed set of n vertices, introduced by Erdős and Rényi in [8] and studied in detail in [9], there is a “characteristic” degree 2m/n: the vertex degrees hav ...
... most basic properties of a graph or network is its degree sequence. For the standard random graph model n m of all graphs with m edges on a fixed set of n vertices, introduced by Erdős and Rényi in [8] and studied in detail in [9], there is a “characteristic” degree 2m/n: the vertex degrees hav ...
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.