scholarly journals SEMIPARAMETRIC STRUCTURAL MODELS OF BINARY RESPONSE: SHAPE RESTRICTIONS AND PARTIAL IDENTIFICATION

2012 ◽  
Vol 29 (2) ◽  
pp. 231-266 ◽  
Author(s):  
Andrew Chesher
Keyword(s):  
Monotone Function ◽  
Single Equation ◽  
Threshold Function ◽  
Constructive Proof ◽  
Binary Response ◽  
Binary Responses ◽  
Explanatory Variables ◽  
Threshold Functions ◽  
Threshold Crossing ◽  
Linear Index

I study the partial identifying power of structural single-equation threshold-crossing models for binary responses when explanatory variables may be endogenous. The sharp identified set of threshold functions is derived for the case in which explanatory variables are discrete, and I provide a constructive proof of sharpness. There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone function of a linear index involving the observable explanatory variables. The restriction brings great computational benefits, allowing calculation of the identified set of index coefficients without calculating the nonparametrically specified threshold function. With the restriction in place, the methods of the paper can be applied to produce identified sets in a class of binary response models with mismeasured explanatory variables.

scholarly journals Monotone Boolean Functions with s Zeros Farthest from Threshold Functions

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Kazuyuki Amano ◽  
Jun Tarui
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Learning Algorithm ◽  
Monotone Function ◽  
Threshold Function ◽  
Binary Representation ◽  
Threshold Functions ◽  
Monotone Boolean Function ◽  
Monotone Boolean Functions ◽  
International Audience

International audience Let $T_t$ denote the $t$-threshold function on the $n$-cube: $T_t(x) = 1$ if $|\{i : x_i=1\}| \geq t$, and $0$ otherwise. Define the distance between Boolean functions $g$ and $h$, $d(g,h)$, to be the number of points on which $g$ and $h$ disagree. We consider the following extremal problem: Over a monotone Boolean function $g$ on the $n$-cube with $s$ zeros, what is the maximum of $d(g,T_t)$? We show that the following monotone function $p_s$ maximizes the distance: For $x \in \{0,1\}^n$, $p_s(x)=0$ if and only if $N(x) < s$, where $N(x)$ is the integer whose $n$-bit binary representation is $x$. Our result generalizes the previous work for the case $t=\lceil n/2 \rceil$ and $s=2^{n-1}$ by Blum, Burch, and Langford [BBL98-FOCS98], who considered the problem to analyze the behavior of a learning algorithm for monotone Boolean functions, and the previous work for the same $t$ and $s$ by Amano and Maruoka [AM02-ALT02].

scholarly journals On Group Comparisons With Logistic Regression Models

2018 ◽  
Vol 49 (2) ◽  
pp. 498-525 ◽  
Author(s):  
Jouni Kuha ◽  
Colin Mills
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Causal Effects ◽  
Binary Response ◽  
Binary Responses ◽  
Logistic Regression Models ◽  
Explanatory Variables ◽  
Continuous Response ◽  
Binary Model ◽  
The Subject

It is widely believed that regression models for binary responses are problematic if we want to compare estimated coefficients from models for different groups or with different explanatory variables. This concern has two forms. The first arises if the binary model is treated as an estimate of a model for an unobserved continuous response and the second when models are compared between groups that have different distributions of other causes of the binary response. We argue that these concerns are usually misplaced. The first of them is only relevant if the unobserved continuous response is really the subject of substantive interest. If it is, the problem should be addressed through better measurement of this response. The second concern refers to a situation which is unavoidable but unproblematic, in that causal effects and descriptive associations are inherently group dependent and can be compared as long as they are correctly estimated.

scholarly journals On Group Comparisons with Logistic Regression Models

2017 ◽  
Author(s):  
Jouni Kuha ◽  
Colin Mills
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Causal Effects ◽  
Binary Response ◽  
Binary Responses ◽  
Logistic Regression Models ◽  
Explanatory Variables ◽  
Continuous Response ◽  
Binary Model ◽  
The Subject

It is widely believed that regression models for binary responses are problematic if we want to compare estimated coefficients from models for different groups or with different explanatory variables. This concern has two forms. The first arises if the binary model is treated as an estimate of a model for an unobserved continuous response, and the second when models are compared between groups which have different distributions of other causes of the binary response. We argue that these concerns are usually misplaced. The first of them is only relevant if the unobserved continuous response is really the subject of substantive interest. If it is, the problem should be addressed through better measurement of this response. The second concern refers to a situation which is unavoidable but unproblematic, in that causal effects and descriptive associations are inherently group-dependent and can be compared as long as they are correctly estimated.

The U. S.-Canada Free Trade Agreement: Impact on the U. S. Steel Industry

1994 ◽  
Vol 38 (1) ◽  
pp. 53-61 ◽  
Author(s):  
Harold R. Williams ◽  
Thomas J. Botzman
Keyword(s):  
Free Trade ◽  
Multiple Linear Regression Model ◽  
Trade Agreement ◽  
Single Equation ◽  
Steel Mill ◽  
Iron And Steel ◽  
Explanatory Variables ◽  
Income Elasticities ◽  
Price And Income Elasticities ◽  
The Impact

This study empirically estimates the impact of the U. S.-Canada FTA on specific iron and steel exports and imports using quarterly data for the period January 1981 to December 1990. A single equation multiple linear regression model is used to quantify at the industry and industry segment levels the impact of the agreement. The dependent variables are the quantities of major steel products traded between the two nations. The explanatory variables include foreign price adjusted for the exchange rate and tariff rate, domestic price, and the industrial production index. Results include calculation of price and income elasticities, which vary considerably by industry segments. The impact of free trade, as modeled, varies widely from product to product. As such it has important implications not only for government policy and employment but also for the adjustment problems faced by both the large integrated steel mill and the minimill producers.

Random high-dimensional orders

1995 ◽  
Vol 27 (01) ◽  
pp. 161-184 ◽  
Author(s):  
Béla Bollobás ◽  
Graham Brightwell
Keyword(s):  
Partial Order ◽  
Rapid Growth ◽  
Entire Range ◽  
Maximum Degree ◽  
Threshold Function ◽  
High Dimensional ◽  
Sharp Threshold ◽  
Threshold Functions

The random k-dimensional partial order P k (n) on n points is defined by taking n points uniformly at random from [0,1] k . Previous work has concentrated on the case where k is constant: we consider the model where k increases with n. We pay particular attention to the height H k (n) of P k (n). We show that k = (t/log t!) log n is a sharp threshold function for the existence of a t-chain in P k (n): if k – (t/log t!) log n tends to + ∞ then the probability that P k (n) contains a t-chain tends to 0; whereas if the quantity tends to − ∞ then the probability tends to 1. We describe the behaviour of H k (n) for the entire range of k(n). We also consider the maximum degree of P k (n). We show that, for each fixed d ≧ 2, is a threshold function for the appearance of an element of degree d. Thus the maximum degree undergoes very rapid growth near this value of k. We make some remarks on the existence of threshold functions in general, and give some bounds on the dimension of P k (n) for large k(n).

STRUCTURAL CONNECTIONIST LEARNING WITH COMPLEMENTARY CODING

1992 ◽  
Vol 03 (01) ◽  
pp. 19-30 ◽  
Author(s):  
AKIRA NAMATAME ◽  
YOSHIAKI TSUKAMOTO
Keyword(s):  
Learning Algorithm ◽  
Internal Representation ◽  
Threshold Function ◽  
Sufficient Condition ◽  
Structural Learning ◽  
Similarity Matrix ◽  
Training Set ◽  
Threshold Functions ◽  
Connectionist Networks ◽  
Hidden Layer

We propose a new learning algorithm, structural learning with the complementary coding for concept learning problems. We introduce the new grouping measure that forms the similarity matrix over the training set and show this similarity matrix provides a sufficient condition for the linear separability of the set. Using the sufficient condition one should figure out a suitable composition of linearly separable threshold functions that classify exactly the set of labeled vectors. In the case of the nonlinear separability, the internal representation of connectionist networks, the number of the hidden units and value-space of these units, is pre-determined before learning based on the structure of the similarity matrix. A three-layer neural network is then constructed where each linearly separable threshold function is computed by a linear-threshold unit whose weights are determined by the one-shot learning algorithm that requires a single presentation of the training set. The structural learning algorithm proceeds to capture the connection weights so as to realize the pre-determined internal representation. The pre-structured internal representation, the activation value spaces at the hidden layer, defines intermediate-concepts. The target-concept is then learned as a combination of those intermediate-concepts. The ability to create the pre-structured internal representation based on the grouping measure distinguishes the structural learning from earlier methods such as backpropagation.

Depletion of retinal dopamine does not affect the ERG b-wave increment threshold function in goldfish in vivo

1994 ◽  
Vol 11 (4) ◽  
pp. 695-702 ◽  
Author(s):  
Zheng-Shi Lin ◽  
Stephen Yazulla
Keyword(s):  
Horizontal Cell ◽  
Threshold Function ◽  
Photopic Vision ◽  
Threshold Functions ◽  
Increment Threshold ◽  
Intensity Response ◽  
Purkinje Shift ◽  
6 Hydroxydopamine ◽  
Fish Retina

AbstractIncrement threshold functions of the electroretinogram (ERG) b–wave were obtained from goldfish using an in vivo preparation to study intraretinal mechanisms underlying the increase in perceived brightness induced by depletion of retinal dopamine by 6–hydroxydopamine (6–OHDA). Goldfish received unilateral intraocular injections of 6–OHDA plus pargyline on successive days. Depletion of retinal dopamine was confirmed by the absence of tyrosine-hydroxylase immunoreactivity at 2 to 3 weeks postinjection as compared to sham-injected eyes from the same fish. There was no difference among normal, sham-injected or 6–OHDA-injected eyes with regard to ERG waveform, intensity-response functions or increment threshold functions. Dopamine-depleted eyes showed a Purkinje shift, that is, a transition from rod-to-cone dominated vision with increasing levels of adaptation. We conclude (1) dopamine-depleted eyes are capable of photopic vision; and (2) the ERG b–wave is not diagnostic for luminosity coding at photopic backgrounds. We also predict that (1) dopamine is not required for the transition from scotopic to photopic vision in goldfish; (2) the ERG b–wave in goldfish is influenced by chromatic interactions; (3) horizontal cell spinules, though correlated with photopic mechanisms in the fish retina, are not necessary for the transition from scotopic to photopic vision; and (4) the OFF pathway, not the ON pathway, is involved in the action of dopamine on luminosity coding in the retina.

Improved Wavelet Thresholding for CCD Measurement Image Denoising

2014 ◽  
Vol 574 ◽  
pp. 432-435 ◽  
Author(s):  
Jie Zhan ◽  
Zhen Xing Li
Keyword(s):  
Image Denoising ◽  
Threshold Function ◽  
Wavelet Thresholding ◽  
Wavelet Coefficients ◽  
Local Correlation ◽  
Thresholding Method ◽  
Threshold Functions ◽  
Soft Threshold ◽  
Simulation Results ◽  
Filtering Effect

An improved wavelet thresholding method is presented and successfully applied to CCD measuring image denoising. On the analysis of the current widely used soft threshold and hard threshold, combining characteristics of the CCD measuring image and use of local correlation of wavelet coefficients, an improved threshold function is proposed, and the denoising results were contrasted among different threshold functions. The simulation results show that adopting the improved threshold function can acquire better filtering effect than traditional soft threshold and hard threshold methods.

Binary response models comparison using the 𝛼-Chernoff divergence measure and exponential integral functions

2021 ◽  
pp. 37-53
Author(s):  
Subir Ghosh ◽  
Hans Nyquist
Keyword(s):  
Probability Distributions ◽  
Binary Response ◽  
Divergence Measure ◽  
Exponential Integral ◽  
Response Models ◽  
Content Type ◽  
Explanatory Variables ◽  
Criterion Functions ◽  
Models Comparison ◽  
Binary Response Models

In this paper, the families of binary response models are describing the data on a response variable having two possible outcomes and p p explanatory variables when the possible responses and their probabilities are functions of the explanatory variables. The α \alpha -Chernoff divergence measure and the Bhattacharyya divergence measure when α = 1 / 2 \alpha = 1/2 are the criterion functions used for quantifying the dissimilarity between probability distributions by expressing the divergence measures in terms of the exponential integral functions. The dependences of odds ratio and hazard function on the explanatory variables are also a part of the modeling.

Optimization of threshold functions over streams

2021 ◽  
Vol 14 (6) ◽  
pp. 878-889
Author(s):  
Walter Cai ◽  
Philip A. Bernstein ◽  
Wentao Wu ◽  
Badrish Chandramouli
Keyword(s):  
Data Stream ◽  
Broad Class ◽  
Threshold Function ◽  
Normal Operation ◽  
Time Interval ◽  
Surprising Result ◽  
Data Stream Management ◽  
Processing Application ◽  
Threshold Functions ◽  
Stream Management

A common stream processing application is alerting, where the data stream management system (DSMS) continuously evaluates a threshold function over incoming streams. If the threshold is crossed, the DSMS raises an alarm. The threshold function is often calculated over two or more streams, such as combining temperature and humidity readings to determine if moisture will form on a machine and therefore cause it to malfunction. This requires taking a temporal join across the input streams. We show that for the broad class of functions called quasiconvex functions, the DSMS needs to retain very few tuples per-data-stream for any given time interval and still never miss an alarm. This surprising result yields a large memory savings during normal operation. That savings is also important if one stream fails, since the DSMS would otherwise have to cache all tuples in other streams until the failed stream recovers. We prove our algorithm is optimal and provide experimental evidence that validates its substantial memory savings.

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