Monotonicity Restrictions Research Articles

Label noise filtering techniques to improve monotonic classification

The monotonic ordinal classification has increased the interest of researchers and practitioners within machine learning community in the last years. In real applications, the problems with monotonicity constraints are very frequent. To construct predictive monotone models from those problems, many classifiers require as input a data set satisfying the monotonicity relationships among all samples. Changing the class labels of the data set (relabeling) is useful for this. Relabeling is assumed to be an important building block for the construction of monotone classifiers and it is proved that it can improve the predictive performance.In this paper, we will address the construction of monotone datasets considering as noise the cases that do not meet the monotonicity restrictions. For the first time in the specialized literature, we propose the use of noise filtering algorithms in a preprocessing stage with a double goal: to increase both the monotonicity index of the models and the accuracy of the predictions for different monotonic classifiers. The experiments are performed over 12 datasets coming from classification and regression problems and show that our scheme improves the prediction capabilities of the monotonic classifiers instead of being applied to original and relabeled datasets. In addition, we have included the analysis of noise filtering process in the particular case of wine quality classification to understand its effect in the predictive models generated.

Non-monetary news in central bank communication

Using evidence from four major central banks, we decompose news conveyed by central-bank communication into news about monetary policy (monetary news), as well as non-monetary news, i.e., news about economic growth and news affecting financial risk premia. Our approach exploits high-frequency comovement of stocks and interest rates combined with monotonicity restrictions across maturities in the yield curve. We find significant differences in the news composition depending on the communication channel used by central banks. Monetary news prevails in policy decision announcements. However, the non-monetary component accounts for more than half of communications that provide context to policy decisions such as press conferences and minutes. We show that non-monetary news drives a significant part of financial markets' reaction during the financial crisis and in the early recovery, while monetary news gains importance since 2013.

Non-Monetary News in Central Bank Communication

We quantify the importance of non-monetary news in central bank communication. Using evidence from four major central banks and a comprehensive classification of events, we decompose news conveyed by central banks into news about monetary policy, economic growth, and separately, shocks to risk premia. Our approach exploits high-frequency comovement of stocks and interest rates combined with monotonicity restrictions across the yield curve. We find significant differences in news composition depending on the communication channel used by central banks. Non-monetary news prevails in about 40% of policy decision announcements by the Fed and the ECB, and this fraction is even higher for communications that provide context to policy decisions such as press conferences. We show that non-monetary news accounts for a significant part of financial markets' reaction during the financial crisis and in the early recovery, while monetary shocks gain importance since 2013.

Semiparametric estimation of panel data models without monotonicity or separability

Nonseparable panel data models with fixed effects have received a great deal of attention in the literature. Monotonicity is a common assumption in these settings, which may be violated in practice. Monotonicity-based estimators are inconsistent and the associated inference misleading under misspecification. In this paper, we propose some semiparametric estimators without imposing the monotonicity restriction. Under regularity conditions, our estimators are consistent and asymptotically normal. Our simulation suggests that our estimators work well in finite samples.

Dyonic configurations in nonlinear electrodynamics coupled to general relativity

We consider static, spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$. After a brief review on black hole (BH) and solitonic solutions, obtained so far with pure electric or magnetic fields, an attempt is made to obtain dyonic solutions, those with both electric and magnetic charges. A general scheme is suggested, leading to solutions in quadratures for an arbitrary Lagrangian function $L(f)$ (up to some monotonicity restrictions); such solutions are expressed in terms of $f$ as a new radial coordinate instead of the usual coordinate $r$. For the truncated Born-Infeld theory (depending on the invariant $f$ only), a general dyonic solution is obtained in terms of $r$. A feature of interest in this solution is the existence of a special case with a self-dual electromagnetic field, $f \equiv 0$ and the Reissner-Nordstr\"om metric.

Markov-switching quantile autoregression: a Gibbs sampling approach

Abstract We extend the class of linear quantile autoregression models by allowing for the possibility of Markov-switching regimes in the conditional distribution of the response variable. We also develop a Gibbs sampling approach for posterior inference by using data augmentation and a location-scale mixture representation of the asymmetric Laplace distribution. Bayesian calculations are easily implemented, because all complete conditional densities used in the Gibbs sampler have closed-form expressions. The proposed Gibbs sampler provides the basis for a stepwise re-estimation procedure that ensures non-crossing quantiles. Monte Carlo experiments and an empirical application to the U.S. real interest rate show that both inference and forecasting are improved when the quantile monotonicity restriction is taken into account.

“When, Where, and How” of Efficiency Estimation: Improved Procedures for Stochastic Frontier Modeling

ABSTRACTThe issues of functional form, distributions of the error components, and endogeneity are for the most part still open in stochastic frontier models. The same is true when it comes to imposition of restrictions of monotonicity and curvature, making efficiency estimation an elusive goal. In this article, we attempt to consider these problems simultaneously and offer practical solutions to the problems raised by Stone and addressed by Badunenko, Henderson and Kumbhakar. We provide major extensions to smoothly mixing regressions and fractional polynomial approximations for both the functional form of the frontier and the structure of inefficiency. Endogeneity is handled, simultaneously, using copulas. We provide detailed computational experiments and an application to U.S. banks. To explore the posteriors of the new models we rely heavily on sequential Monte Carlo techniques.

Nonparametric Knn estimation with monotone constraints

ABSTRACTThe K-nearest-neighbor (Knn) method is known to be more suitable in fitting nonparametrically specified curves than the kernel method (with a globally fixed smoothing parameter) when data sets are highly unevenly distributed. In this paper, we propose to estimate a nonparametric regression function subject to a monotonicity restriction using the Knn method. We also propose using a new convergence criterion to measure the closeness between an unconstrained and the (monotone) constrained Knn-estimated curves. This method is an alternative to the monotone kernel methods proposed by Hall and Huang (2001), and Du et al. (2013). We use a bootstrap procedure for testing the validity of the monotone restriction. We apply our method to the “Job Market Matching” data taken from Gan and Li (2016) and find that the unconstrained/constrained Knn estimators work better than kernel estimators for this type of highly unevenly distributed data.

Integrated-Quantile-Based Estimation for First-Price Auction Models

This article considers nonparametric estimation of first-price auction models under the monotonicity restriction on the bidding strategy. Based on an integrated-quantile representation of the first-order condition, we propose a tuning-parameter-free estimator for the valuation quantile function. We establish its cube-root-n consistency and asymptotic distribution under weaker smoothness assumptions than those typically assumed in the empirical literature. If the latter are true, we also provide a trimming-free smoothed estimator and show that it is asymptotically normal and achieves the optimal rate of Guerre, Perrigne, and Vuong (2000). We illustrate our method using Monte Carlo simulations and an empirical study of the California highway procurement auctions. Supplementary materials for this article are available online.

Positive solutions of superlinear and sublinear boundary value problems

We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.

Композиційно-номінативні модальні логіки немонотонних часткових предикатів та їх числення

We consider new program-oriented logical formalisms of modal type – pure first-order composition nominative modal logics of partial predicates without monotonicity restriction. For such logics we specify semantic models and languages and investigate interactions of modal compositions with renominations and quantifiers. A consequence relation for two formulas in a given state is introduced and generalized to a logical consequence relation for two sets of formulas specified with states. We describe properties of a logical consequence relation for sets of formulas specified with states and properties of modalities elimination for various reachability relations. Sequent type calculi are proposed for general transitional and temporal modal logics of non-monotone predicates. We define various types of the calculi for different reachability relations and specify their basic sequent forms and sequent closure conditions. We give a step-by-step description of a deriving process (building of a sequent tree) by the introduced calculi. For these calculi we prove the soundness theorem and the theorem about existence of a counter-model for a non-closed path in a sequent tree. The counter-model is obtained using the Hintikka sets method. The proof of the completeness theorem is based on the theorem about existence of a counter-model. Problems in programming 2017; 2: 24-39

Pre-classifier adjectival modification in Mandarin Chinese: a measurement-based analysis

Pre-classifier adjectival modification (PCAM) structures in Mandarin Chinese are subject to some unique constraints, such as: (i) only size adjectives are allowed; (ii) the pre-classifier adjectives resist further adverbial modification by degree adverbs and reduplicated forms of their own. This cluster of phenomena is explained in a measurement-based analysis. It is hypothesized that the pre-classifier adjectives introduce a measure function, which has some non-trivial order-preserving property and is constrained by a monotonicity restriction: what is measured must respect part-of relations. This analysis correctly predicts that only those classifiers and nouns that are associated with monotonic dimensions can be accessed by size adjectives, thus providing a motivated account of the elusive contrast between expressions like yi da tiao yu ‘one big Cl fish’ and *yi da wei laoshi ‘one big Cl teacher.’ And in so doing, the present analysis brings PCAM structures closer to some other constructions that make use of the same grammar of measurement across categories.

Monotone support vector quantile regression

ABSTRACTQuantile regression (QR) models have received a great deal of attention in both the theoretical and applied statistical literature. In this paper we propose support vector quantile regression (SVQR) with monotonicity restriction, which is easily obtained via the dual formulation of the optimization problem. We also provide the generalized approximate cross validation method for choosing the hyperparameters which affect the performance of the proposed SVQR. The experimental results for the synthetic and real data sets confirm the successful performance of the proposed model.

Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

ABSTRACTThis paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.

Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective.

The fitness concept and perforce the definition of frequency independent fitnesses from population genetics is closely tied to discrete time population models with non-overlapping generations. Evolutionary ecologists generally focus on trait evolution through repeated mutant substitutions in populations with complicated life histories. This goes with using the per capita invasion speed of mutants as their fitness. In this paper we develop a concept of frequency independence that attempts to capture the practical use of the term by ecologists, which although inspired by population genetics rarely fits its strict definition. We propose to call the invasion fitnesses of an eco-evolutionary model frequency independent when the phenotypes can be ranked by competitive strength, measured by who can invade whom. This is equivalent to the absence of weak priority effects, protected dimorphisms and rock–scissor–paper configurations. Our concept differs from that of Heino et al. (TREE 13:367–370, 1998) in that it is based only on the signs of the invasion fitnesses, whereas Heino et al. based their definitions on the structure of the feedback environment, summarising the effect of all direct and indirect interactions between individuals on fitness. As it turns out, according to our new definition an eco-evolutionary model has frequency independent fitnesses if and only if the effect of the feedback environment on the fitness signs can be summarised by a single scalar with monotonic effect. This may be compared with Heino et al.’s concept of trivial frequency dependence defined by the environmental feedback influencing fitness, and not just its sign, in a scalar manner, without any monotonicity restriction. As it turns out, absence of the latter restriction leaves room for rock–scissor–paper configurations. Since in ‘realistic’ (as opposed to toy) models frequency independence is exceedingly rare, we also define a concept of weak frequency dependence, which can be interpreted intuitively as almost frequency independence, and analyse in which sense and to what extent the restrictions on the potential model outcomes of the frequency independent case stay intact for models with weak frequency dependence.

Identification and estimation of endogenous selection models in the presence of misclassification errors

This paper shows the semi-parametric identification and estimation of sample selection models when the primary equation contains a discrete mismeasured endogenous covariate. Assuming that appropriate instruments for the presence of endogeneity are available, I apply a control function approach to remove the possible endogeneity. Based on the conditional mean independence between the model error and the selection error, the model can be regarded as a semi-parametric regression model with a discrete mismeasured covariate, thereby permitting a non-classical measurement error. Additional identification assumptions include monotonicity restrictions on the regression function and an empirical testable rank condition. I then use the identification result to construct a sieve maximum likelihood estimation estimator to estimate the model parameters consistently and recover the selection rule and joint probabilities of the accurately measured endogenous variable and the mismeasured observed variable. The proposed estimation method allows for a rather flexible functional form of the mismeasured endogenous covariate, requires only one valid instrument to control for both endogeneity and measurement errors for the variable of interest, and imposes no distribution assumptions on the selection rule.

Adaptive testing on a regression function at a point

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of H\"{o}lder classes, up to a $\log\log n$ term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary and the proportion of true null hypotheses in a multiple testing problem.

Monotonic Random Forest with an Ensemble Pruning Mechanism based on the Degree of Monotonicity

In classification problems, it is very common to have ordinal data in the variables, in both explanatory and class variables. When the class variable should increase according to a subset of explanatory variables, the problem must satisfy the monotonicity constraint. It is well known that standard classification tree algorithms, such as CART or C4.5, are not guaranteed to produce monotonic trees, even if the data set is completely monotone. Recently, some classifiers have been designed to handle these kinds of problems. In decision trees, growing and pruning mechanisms have been updated to improve the monotonicity of the trees. In this paper, we study the suitability of using these mechanisms in the generation of Random Forests. For this, we propose a simple ensemble pruning mechanism based on the degree of monotonicity of the resulting trees. The performance of several decision trees are evaluated through experimental studies on monotonic data sets. We deduce that the trees produced by the Random Forest also hold the monotonicity restriction but achieve a slightly better predictive performance than standard algorithms.

Identification of Nonseparable Triangular Models With Discrete Instruments

We study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable. Using group and dynamical systems theories, we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition, even if the instrument is discrete. When identified, the model is also testable. Our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions.

Adaptive Testing on a Regression Function at a Point

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary, and the proportion of true null hypotheses in a multiple testing problem.