Top PDF Minimum distance histograms with universal performance guarantees

Minimum distance histograms with universal performance guarantees

Minimum distance histograms with universal performance guarantees

Received: 31 December 2018 / Accepted: 12 June 2019 / Published online: 13 July 2019 © The Author(s) 2019 Abstract We present a data-adaptive multivariate histogram estimator of an unknown density f based on n independent samples from it. Such histograms are based on binary trees called regular pavings (RPs). RPs represent a computationally convenient class of simple functions that remain closed under addition and scalar multiplication. Unlike other density estimation methods, including various regularization and Bayesian methods based on the likelihood, the minimum distance estimate (MDE) is guar- anteed to be within an L 1 distance bound from f for a given n, no matter what the underlying f happens to be, and is thus said to have universal performance guaran- tees (Devroye and Lugosi, Combinatorial methods in density estimation. Springer, New York, 2001 ). Using a form of tree matrix arithmetic with RPs, we obtain the first generic constructions of an MDE, prove that it has universal performance guar- antees and demonstrate its performance with simulated and real-world data. Our main contribution is a constructive implementation of an MDE histogram that can handle large multivariate data bursts using a tree-based partition that is computa- tionally conducive to subsequent statistical operations.
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Performance guarantees for distributed reachability queries

Performance guarantees for distributed reachability queries

4. DISTRIBUTED BOUNDED REACHA- BILITY QUERIES We next develop a distributed evaluation algorithm for bounded reachability queries q br (s, t, l), to decide whether dist(s, t) ≤ l. In contrast to reachability queries, to evaluate q br (s, t, l) we need to keep track of the distances for all pairs of nodes involved. Nevertheless, we show that the algorithm has the same performance guarantees as algorithm disReach. Theorem 2: Over a fragmentation F = (F, G f ) of a graph G, bounded reachability queries can be evaluated with the same performance guarantees as for reachability queries. ✷ To prove Theorem 2, we outline an algorithm, denoted by disDist (not shown), for evaluating q br (s, t, l) over a fragmen- tation F of a graph G. It is similar to algorithm disReach for reachability queries (Fig. 3), but it needs different strategies for partial evaluation at individual sites and for assembling partial answers at the coordinator site. These are carried out by procedures localEval d and evalDG d , respectively. Procedure localEval d . To evaluate q br (s, t, l), for each frag- ment F i and each in-node v in F i , we need to find dist(v, t), the distance from v to t. To do this, we find the minimum value of dist(v, v ′ ) + dist(v ′ , t) when v ′ ranges over all virtual nodes in F i to which v can reach. We associate a variable
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Towards practical minimum-entropy universal decoding

Towards practical minimum-entropy universal decoding

Using properly constructed expander codes as discussed in [19], we may select component codes of the expander code to have good min-max distance so that the aggregate code has good min-max distance. We can then show that the performance of the above mentioned algorithm is provably good (has a positive error exponent). In fact, from [1], it follows that if we take as our component code of the expander code to be a random binary linear code chosen uniformly, then with exponentially high probability the distance spectrum of the code will satisfy our ‘minimum-maximum distance’ criterion.
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Learning Nonstructural Distance Metric by Minimum Cluster Distortion

Learning Nonstructural Distance Metric by Minimum Cluster Distortion

There remains some future directions for re- search. First, as we stated in section 4.3, the effect of a cluster weighted generalized metric must be in- vestigated and optimal weighting must be induced. Second, as noted in section 5.2.1, the dimensional- ity reduction required for linguistic data may con- strain the performance of the metric distance. To alleviate this problem, simultaneous dimensionality reduction and metric induction may be necessary, or the same idea in a kernel-based approach is worth considering. The latter obviates the problem of di- mensionality, while it restricts the usage to a situa- tion where the kernel-based approach is available. 7 Conclusion
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A practical minimum distance method for syntax error handling

A practical minimum distance method for syntax error handling

The Minimum Distance Recovery Method is practical in both time (O(n)) and space, requiring only a minor amount of storage for string representations of the CFG terminal symbols, in addition to the usual storage for LR parsers. It has been used in language compilers which run with normal memory requirements and with acceptable response times on various computers (DEC VAX/750, SUN 3 and SUN 4). There is no eect on the analysis of correct input, as the recovery method is only invoked when the parser detects an error. The parser proceeds exactly as normal on correct input, with no overheads.
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The Minimum Universal Cost Flow in an Infeasible Flow Network

The Minimum Universal Cost Flow in an Infeasible Flow Network

In such a case, S is called isolation by Greenberg [2] and a witness by Aggarwal, Hao and Orlin [3]. Aggarwal et al. [3] showed that the problem of finding a minimum witness in an infeasible flow network is Np- hard. But rather efficient heuristic procedures have been introduced for practical instances, Greenberg [2,4,5].

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Minimum Distance Requirements and Liability: Implications for Co Existence

Minimum Distance Requirements and Liability: Implications for Co Existence

In this paper, we analyze the value of planting transgenic crops when farmers face ex-ante regulatory and ex-post liability costs under irreversibility and uncertainty. The regulatory instrument analyzed is the minimum distance to neighbouring fields. First results indicate that under irreversibility and uncertainty the value of cultivating transgenic crops presents a trade- off between ex-ante regulatory and ex-post liability costs with respect to farm size. From this, it is not possible to conclude a priori the net effect on the size of the adopting farms, if, ceteris paribus, a minimum distance regulation is adopted within the EU and farmers can be held liable ex-post.
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On  the  Minimum  Number  of  Multiplications  Necessary  for  Universal  Hash  Constructions

On the Minimum Number of Multiplications Necessary for Universal Hash Constructions

We provide a brief survey on the lower bound of multiplications for computing a polynomial. Note that our interest in this paper is to provide a lower bound on number of multiplications for computing a multi variate polynomial which is an universal hash. Even though these two issues are very much related (some of the ideas in proving results are also similar), some immediate differences can be noted. For example, the existing bounds depend on the degree of the polynomials whereas we provide bound on the number of message blocks (degree could be arbitrarily higher). The existing works consider multivariate polynomials which has a special form: P (a 0 , . . . , a n , x 1 , . . . , x m ) := a 0 + P n i=1 a i · Φ i (x 1 , x 2 , . . . , x m )
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Statistical Guarantees of Performance for MIMO Designs

Statistical Guarantees of Performance for MIMO Designs

Sources of noise such as quantization, introduce randomness into Register Transfer Level (RTL) designs of Multiple Input Multiple Output (MIMO) systems. Performance of these MIMO RTL designs is typically quantified by metrics averaged over simulations. In this paper, we introduce a formal approach to compute these metrics with high confidence. We define best, bounded and average case performance metrics as properties in a probabilistic temporal logic. We then use probabilistic model checking to verify these properties for MIMO RTL and thereby guarantee the statistical performance. However, probabilistic model checking is known to encounter the problem of state space explosion. With respect to the properties of interest, we show sound and efficient reductions that significantly improve the scalability of our approach. We illustrate our approach on different non-trivial components of MIMO system designs.
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Statistical guarantees of performance for RTL designs

Statistical guarantees of performance for RTL designs

• In sequential designs, each state in the corresponding DTMC is a concatenation of the present input values and the internal state of the design. We shall describe these DTMCs in more detail in Section 3.4.1. In our SHARPE methodology, the steps for performing formal probabilistic analysis on sequential designs are as follows. We convert a sequential RTL module into a DTMC [21] with the transition probabilities derived from the signal probability distributions and information obtained from the lower levels of implementation. We express the performance metrics of our interest as properties in probabilistic computational tree logic (pCTL) [22]. Finally, we use a probabilistic model checking engine, PRISM [23], to compute the required probabilistic invariants. Probabilistic model checking explores all possible DTMC sequences that are relevant to the property, and therefore the computation of the probabilistic invariant is high in confidence.
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Long Distance Dependencies and Applicative Universal Grammar

Long Distance Dependencies and Applicative Universal Grammar

Long Distance Dependencies and Applicative Universal Grammar Long Distance Dependencies and Applicative Universal Grammar Sel)astian Shaumyan Yale University, U S A , e maih shaumyan@minerva cis yale[.]

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Generalized Minimum Perpendicular Distance Square Method of Estimation

Generalized Minimum Perpendicular Distance Square Method of Estimation

In case of heteroscedasticity, a Generalized Minimum Perpendicular Distance Square (GMPDS) method has been sug- gested instead of traditionally used Generalized Least Square (GLS) method to fit a regression line, with an aim to get a better fitted regression line, so that the estimated line will be closest one to the observed points. Mathematical form of the estimator for the parameters has been presented. A logical argument behind the relationship between the slopes of the lines Y ˆ i   ˆ 0   ˆ 1 X i and X ˆ i   ˆ 0    ˆ 1  Y i has been placed.
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Achieving Performance and Availability Guarantees with Spot Instances

Achieving Performance and Availability Guarantees with Spot Instances

Abstract—In the Infrastructure-as-a-Service (IaaS) cloud com- puting market, spot instances refer to virtual servers that are rented via an auction. Spot instances allow IaaS providers to sell spare capacity while enabling IaaS users to acquire virtual servers at a lower pricer than the regular market price (also called “on demand” price). Users bid for spot instances at their chosen limit price. Based on the bids and the available capacity, the IaaS provider sets a clearing price. A bidder acquires their requested spot instances if their bid is above the clearing price. However, these spot instances may be terminated by the IaaS provider impromptu if the auction’s clearing price goes above the user’s limit price. In this context, this paper addresses the following question: Can spot instances be used to run paid web services while achieving performance and availability guaran- tees? The paper examines the problem faced by a Software-as- a-Service (SaaS) provider who rents spot instances from an IaaS provider and uses them to provide a web service on behalf of a paying customer. The SaaS provider incurs a monetary cost for renting computing resources from the IaaS provider, while charging its customer for executing web service transactions and paying penalties to the customer for failing to meet performance and availability objectives. To address this problem, the paper proposes a bidding scheme and server allocation policies designed to optimize the average revenue earned by the SaaS provider per time unit. Experimental results show that the proposed approach delivers higher revenue to the SaaS provider than an alternative approach where the SaaS provider runs the web service using “on demand” instances. The paper also shows that the server allocation policies seamlessly adapt to varying market conditions, traffic conditions, penalty levels and transaction fees.
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Comparison of Misspecified Calibrated Models: The Minimum Distance Approach

Comparison of Misspecified Calibrated Models: The Minimum Distance Approach

We apply our methodology to compare two standard monetary business cycle models: the cash-in-advance (CIA) model, and the Lucas (1990) and Fuerst (1992) model with portfolio adjustment costs (PAC). The two models have the same un- derlying structure except for the information sets that agents possess when making their decisions. We judge the performance of the models based on their ability to replicate the response of in‡ation and output growth to an unanticipated monetary shock in the U.S. data. A structural vector autoregression (SVAR) is employed to obtain model-free estimates of such impulse responses. We …nd that the null hypoth- esis that CIA and PAC models have the same …t cannot be rejected. We therefore conclude that the frictions underlying the PAC model do not play a signi…cant role in approximating the in‡ation-output dynamics.
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Performance Bonds, Bankers' Guarantees, and the Mareva Injunction

Performance Bonds, Bankers' Guarantees, and the Mareva Injunction

join payment of a demand bond or bank guarantee unless the party seek- ing the injunction can show that the demand on the bond or guarantee is fraudulent and that the bank [r]

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Computable performance guarantees for compressed sensing matrices

Computable performance guarantees for compressed sensing matrices

and the previous works [3, 8] are focusing on worst-case performance guarantee (recovering all the possible k -sparse signals), while the research on phase transition is considering the average-case performance guarantee for a single k -sparse signal with fixed support and sign pattern. Secondly, the phase transition bounds are mostly for random matrices. Hence, for a given deterministic sensing matrix, phase transition results cannot be used for that particular matrix.

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Evaluation of the Queensland Minimum Passing Distance Road Rule

Evaluation of the Queensland Minimum Passing Distance Road Rule

2. Assessment of the extent of compliance with the rule at a range of sites after the commencement of the trial (compliance analysis). 5.1.1 Pre-post comparison As noted earlier in this report, there was no systematic collection of baseline data before the commencement of the trial. The evaluation framework (Haworth et al., 2014) had identified several sets of video observations of cyclists that had previously been commissioned by TMR or Brisbane City Council (see Appendix 2 of the framework report). Video data collected at six inner-city Brisbane locations by TMR as part of cordon counts of bicycle activity appeared to be the most promising pre-data for the MPD evaluation. All of these sites had speed limits of 60 km/h or less. It was decided to collect post-implementation data at these locations and then compare the mean passing distance and percentage of passing distances which were less than required by the road rule for the pre-trial and post-implementation observations at the same sites.
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Global Robustness Evaluation of Deep Neural Networks with Provable Guarantees for the Hamming Distance

Global Robustness Evaluation of Deep Neural Networks with Provable Guarantees for the Hamming Distance

In addition to providing anytime upper/lower bounds on global robustness, our method also guarantees conver- gence. Existing approaches that offer guarantees instead focus on local (pointwise) robustness. These include re- duction to constraint solving [Pulina and Tacchella, 2010; Katz et al., 2017], abstract interpretation [Gehr et al., 2018; Mirman et al., 2018], exhaustive search [Huang et al., 2017] or Monte Carlo tree search (MCTS) for Lipschitz networks [Wu et al., 2018]. Another group of papers considers the prob- lem of whether an output value of a DNN is reachable from a given input subspace [Lomuscio and Maganti, 2017; Ruan et al., 2018a; Dutta et al., 2017], by either reducing the problem to a MILP problem [Lomuscio and Maganti, 2017], or by considering the range of values [Dutta et al., 2017], or by employing global optimisation [Ruan et al., 2018a]. We also mention [Peck et al., 2017], who compute a lower bound of local robustness for the L 2 norm. This is incomparable with
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Testing variants of minimum distance controlled tabular adjustment

Testing variants of minimum distance controlled tabular adjustment

As CTA is discussed as an alternative to well established cell suppression, we also included a qual- ity criterion that allows direct comparison of the performance of CTA to cell suppression, to some extent. First results are promising, indicating that it may be possible to make CTA procedures provide at least as much data meeting the high data quality standards of offi cial statistics for data of a certain relevance as cell suppression. We also suggested restricted RCTA as an option to combine cell sup- pression and CTA, or to facilitate use of CTA in the context of linked tables. RCTA allows to control relative and absolute deviations more precisely than CTA. Unfortunately, RCTA is more sensible to the protection sense (“upper” or “lower”) of sensitive cells than CTA, leading to infeasibility prob- lems. Several strategies have been discussed for a proper choice of protection sense, leading to both optimal and heuristic solutions. Heuristic solutions are likely to be the best practical option, since they will provide a reasonable quality protected table within reasonable time. All these approaches for RCTA are currently under development by the authors.
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The Riemannian Minimum Distance to Means Field Classifier

The Riemannian Minimum Distance to Means Field Classifier

The computational cost of the RMDMF as compared to the RMDM is increased proportionally to the number of means used to populate the means field. Since the computational complexity of Riemannian classifiers is cubic on the size of the covariance matrices used to encode the EEG data, this does not represent a substantial additional cost. When the dimension of the covariance matrices is high, it can be reduced by well-known methods such as principal component analysis or by methods inspired by Riemannian geometry [27, 28]. As reported in [6], the performance of the MDM drops in high dimension, therefore in these situations a dimensionality reduction step in practice is necessary. The RMDMF may turn more robust than the RMDM also with respect to the dimensionality. Further research is necessary to verify these hypotheses.
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