A flexible class of dependence-aware multi-label loss functions

The idea to exploit label dependencies for better prediction is at the core of methods for multi-label classification (MLC), and performance improvements are normally explained in this way. Surprisingly, however, there is no established methodology that allows to analyze the dependence-awareness of MLC algorithms. With that goal in mind, we introduce a class of loss functions that are able to capture the important aspect of label dependence. To this end, we leverage the mathematical framework of non-additive measures and integrals. Roughly speaking, a non-additive measure allows for modeling the importance of correct predictions of label subsets (instead of single labels), and thereby their impact on the overall evaluation, in a flexible way. The well-known Hamming and subset 0/1 losses are rather extreme special cases of this function class, which give full importance to single label sets or the entire label set, respectively. We present concrete instantiations of this class, which appear to be especially appealing from a modeling perspective. The assessment of multi-label classifiers in terms of these losses is illustrated in an empirical study, clearly showing their aptness at capturing label dependencies. Finally, while not being the main goal of this study, we also show some preliminary results on the minimization of this parametrized family of losses.

Sign-rank Can Increase under Intersection

The communication class UPP cc is a communication analog of the Turing Machine complexity class PP . It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f , let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPP cc ( f ) = O (log n ), and UPP cc ( f ∧ f ) = Θ (log 2 n ). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPP cc , the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity n Omega Ω(log n ) . This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time.

Finding Fair and Efficient Allocations for Matroid Rank Valuations

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

Multivalent Prestarlike Functions with Respect to Symmetric Points

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits Under Realizability

We consider the general (stochastic) contextual bandit problem under the realizability assumption, that is, the expected reward, as a function of contexts and actions, belongs to a general function class [Formula: see text]. We design a fast and simple algorithm that achieves the statistically optimal regret with only [Formula: see text] calls to an offline regression oracle across all T rounds. The number of oracle calls can be further reduced to [Formula: see text] if T is known in advance. Our results provide the first universal and optimal reduction from contextual bandits to offline regression, solving an important open problem in the contextual bandit literature. A direct consequence of our results is that any advances in offline regression immediately translate to contextual bandits, statistically and computationally. This leads to faster algorithms and improved regret guarantees for broader classes of contextual bandit problems.

Coefficient estimates for Libera type bi-close-to-convex functions

In a very recent paper, Wang and Bulut [A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876–880] determined the estimates for the general Taylor-Maclaurin coefficients of functions belonging to the bi-close-to-convex function class. In this study, we introduce the class of Libera type bi-close-to-convex functions and obtain the upper bounds for the coefficients of functions belonging to this class. Our results generalize the results in the above mentioned paper.

Etodolac improves collagen induced rheumatoid arthritis in rats by inhibiting synovial inflammation, fibrosis and hyperplasia

Synovial hyperplasia is the main cause of chronic rheumatoid arthritis (RA), but the mechanism of synovial hyperplasia is still unclear. Etodolac (ETD) is a selective COX-2 inhibitor for relieving pain and stiffness in RA, but the disease modifying effect is still lack of evidence. Proteomics method was used to study the differential proteome of synovial tissue in collagen induced arthritis (CIA) in rats. With the help of STRING analysis, the upregulated proteins enriched in the cluster of complement and coagulation cascades and platelet degranulation were highlighted, these proteins with fibrogenic factors Lum, CIV, CXI and Tgfbi participated in the synovial inflammation, fibrosis and hyperplasia in CIA. Based on KOG function class analysis, the proteins involved in the events of the central dogma was explored. They might be hyperplasia related proteins for most of them are related to the proliferation of cancer. ETD significantly attenuated synovial inflammation, fibrosis and hyperplasia in CIA rats by downregulating these proteins. Several proteins have not been observed in RA so far, such as Tmsb4x, Pura, Nfic, Ruvbl1, Snrpd3, U2af2, Srrm2, Srsf7, Elavl1, Hnrnph1, Wars, Yars, Bzw2, Mcts1, Eif4b, Ctsh, Lamp1, Dpp7, Ptges3, Cdc37 and Septin9, they might be potentials targets for RA. Blood biochemistry tests showed the safety of 7 months use of ETD on rats. In conclusion, present study displayed a comprehensive mechanism of synovial hyperplasia in CIA rats, on this basis, the clinical value of ETD in the treatment of RA was well confirmed.