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Register a new userOne-sided versus two-sided stochastic descriptions
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Aernout Coert Daniel van Enter
Publication date
2018
fields
Physics
and research's language is
English
Authors
Aernout C.D. van Enter
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It is well-known that discrete-time finite-state Markov Chains, which are described by one-sided conditional probabilities which describe a dependence on the past as only dependent on the present, can also be described as one-dimensional Markov Fields, that is, nearest-neighbour Gibbs measures for finite-spin models, which are described by two-sided conditional probabilities. In such Markov Fields the time interpretation of past and future is being replaced by the space interpretation of an interior volume, surrounded by an exterior to the left and to the right. If we relax the Markov requirement to weak dependence, that is, continuous dependence, either on the past (generalising the Markov-Chain description) or on the external configuration (generalising the Markov-Field description), it turns out this equivalence breaks down, and neither class contains the other. In one direction this result has been known for a few years, in the opposite direction a counterexample was found recently. Our counterexample is based on the phenomenon of entropic repulsion in long-range Ising (or Dyson) models.
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Given a finite point set $Psubsetmathbb{R}^d$, we call a multiset $A$ a one-sided weak $varepsilon$-approximant for $P$ (with respect to convex sets), if $|Pcap C|/|P|-|Acap C|/|A|leqvarepsilon$ for every convex set $C$. We show that, in contrast with the usual (two-sided) weak $varepsilon$-approximants, for every set $Psubset mathbb{R}^d$ there exists a one-sided weak $varepsilon$-approximant of size bounded by a function of $varepsilon$ and $d$.
In this paper, we study the problem of privacy-preserving data sharing, wherein only a subset of the records in a database are sensitive, possibly based on predefined privacy policies. Existing solutions, viz, differential privacy (DP), are over-pessimistic and treat all information as sensitive. Alternatively, techniques, like access control and personalized differential privacy, reveal all non-sensitive records truthfully, and they indirectly leak information about sensitive records through exclusion attacks. Motivated by the limitations of prior work, we introduce the notion of one-sided differential privacy (OSDP). We formalize the exclusion attack and we show how OSDP protects against it. OSDP offers differential privacy like guarantees, but only to the sensitive records. OSDP allows the truthful release of a subset of the non-sensitive records. The sample can be used to support applications that must output true data, and is well suited for publishing complex types of data, e.g. trajectories. Though some non-sensitive records are suppressed to avoid exclusion attacks, our experiments show that the suppression results in a small loss in utility in most cases. Additionally, we present a recipe for turning DP mechanisms for answering counting queries into OSDP techniques for the same task. Our OSDP algorithms leverage the presence of non-sensitive records and are able to offer up to a 25x improvement in accuracy over state-of-the-art DP-solutions.
This paper is an attempt to deal with the recent realization (Vazirani, Yannakakis 2021) that the Hylland-Zeckhauser mechanism, which has remained a classic in economics for one-sided matching markets, is likely to be highly intractable. HZ uses the power of a pricing mechanism, which has endowed it with nice game-theoretic properties. Hosseini and Vazirani (2021) define a rich collection of Nash-bargaining-based models for one-sided and two-sided matching markets, in both Fisher and Arrow-Debreu settings, together with implementations using available solvers, and very encouraging experimental results. This naturally raises the question of finding efficient combinatorial algorithms for these models. In this paper, we give efficient combinatorial algorithms based on the techniques of multiplicative weights update (MWU) and conditional gradient descent (CGD) for several one-sided and two-sided models defined in HV 2021. Additionally, we define for the first time a Nash-bargaining-based model for non-bipartite matching markets and solve it using CGD. Furthermore, in every case, we study not only the Fisher but also the Arrow-Debreu version; the latter is also called the exchange version. We give natural applications for each model studied. These models inherit the game-theoretic and computational properties of Nash bargaining. We also establish a deep connection between HZ and the Nash-bargaining-based models, thereby confirming that the alternative to HZ proposed in HV 2021 is a principled one.
We investigate the problem of fair recommendation in the context of two-sided online platforms, comprising customers on one side and producers on the other. Traditionally, recommendation services in these platforms have focused on maximizing customer satisfaction by tailoring the results according to the personalized preferences of individual customers. However, our investigation reveals that such customer-centric design may lead to unfair distribution of exposure among the producers, which may adversely impact their well-being. On the other hand, a producer-centric design might become unfair to the customers. Thus, we consider fairness issues that span both customers and producers. Our approach involves a novel mapping of the fair recommendation problem to a constrained version of the problem of fairly allocating indivisible goods. Our proposed FairRec algorithm guarantees at least Maximin Share (MMS) of exposure for most of the producers and Envy-Free up to One item (EF1) fairness for every customer. Extensive evaluations over multiple real-world datasets show the effectiveness of FairRec in ensuring two-sided fairness while incurring a marginal loss in the overall recommendation quality.
Let $n$ be an integer greater or equal than $3$. We give a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, and we call it one-sided $n$-suspended categories. One-sided $n$-angulated categories are also examples of one-sided $n$-suspended categories. We provide a general framework for passing from one-sided $n$-suspended categories to one-sided $n$-angulated categories. Besides, we give a method to construct $n$-angulated quotient categories from Frobenius $n$-prile categories. These results generalize their works by Jasso for $n$-exact categories, Lin for $(n+2)$-angulated categories and Li for one-sided suspended categories.
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