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On the Wikipedia page about naive Bayes classifiers, there is this line:
$p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)
How can a value $>1$ be OK? I thought all probability values were expressed in the range $0 \leq p \... |
I was thinking about CI and subjective Bayesian and I have following two questions:
If a subjective (not objective) Bayesian would care if her predictions don't do well in the real world.
A classical statistician would not care if her confidence statement is (obviously) wrong for a given data set (as in Welch's Parado... |
Quantum Mechanics has generalized probability theory to negative/imaginary numbers, mostly to explain interference patterns, wave/particle duality and generally weird things like that. It can be seen more abstractly, however, as a noncommutative generalisation of Bayesian probability (quote from Terrence Tao). I'm curi... |
I have heard the terms training and validating a model. I know that we select variables which are most statistically significant and we look for other things like multicollinearity. My question is:
what does traning a model involves more than this ?
|
I know about $r^2$ tells you about the amount of variation that can be explained by the predictor variables. I have run a model in which the rsquare has value 0.3010 but has false positive rate of around 15.60%. So this model which is logit in nature predicts 84% cases right. I want to know two things:
1) Is this false... |
We are often interested in estimating the limiting distribution of a parameter in situations where the data exhibit dependence within clusters. For example, a study of the effects of a household-level treatment on household-level outcomes must contend with the possibility that households within villages will have corre... |
I am designing a questionnaire for my dissertation. I am in the process of validating the questionnaire I have applied a Cronbach's alpha test to the initial sample group. The responses to the questionnaire are on a Likert scale; can anyone suggest any further tests to apply to help test its validity. I am not an exp... |
My problem with understanding this expression might come from the fact that English is not my first language, but I don't understand why it's used in this way.
The marginal mean is typically the mean of a group or subgroup's measures of a variable in an experiment, but why not just use the word mean? What's the margina... |
How can I calculate the truncated or trimmed mean? Let's say truncated by 10%?
I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
|
I would like to automate the choice of burn-in for an MCMC chain, e.g. by removing the first n rows based on a convergence diagnostic.
To what extent can this step be safely automated? Even if I still double check the autocorrelation, mcmc trace, and pdfs, it would be nice to have the choice of burn-in length automate... |
I work in the field of data mining and have had very little formal schooling in statistics. Lately I have been reading a lot of work that focuses on Bayesian paradigms for learning and mining, which I find very interesting.
My question is (in several parts), given a problem is there a general framework by which it is... |
This relates to a previous question of mine which didn't gain many responses, perhaps because it wasn't very clear nd well written. I hope this time I will be more accurate and get your much appreciated assistance.
I am analyzing results of a biological experiment. The results given as a single value ( non-negative int... |
I have a process which writes statistics from a server system to a file each second in this format:
label1 label2 label3
344 666 787
344 849 344
939 994 344
There are a number of different values which I need graphs for, and each value is added to the bottom of the file each second.
I am looking for a nice way to sho... |
I recently read Skillicorn's book on matrix decompositions, and was a bit disappointed, as it was targeted to an undergraduate audience. I would like to compile (for myself and others) a short bibliography of essential papers (surveys, but also breakthrough papers) on matrix decompositions. What I have in mind primaril... |
In what circumstances should one consider using regularization methods (ridge, lasso or least angles regression) instead of OLS?
In case this helps steer the discussion, my main interest is improving predictive accuracy.
|
I have a sensor which is capturing accelerometer data as a person walks. What I'm interested in extracting is each signal fragment when a step is taken. The Z-axis is what is used since only one axis is required to detect changes in steps. The images below illustrates a sample Z-axis gait signal (for 400 iterations).
... |
I would like build a web application using R. I am using Windows Vista and have an Apache server. I have tried Rpad, but I was not able to correctly configure it. How do I set up Rpad as I am not that well off with PHP and Apache server? Or are there other ways to use R on Apache server?
|
I am looking for an intuitive explanation of the bias-variance tradeoff, both in general and specifically in the context of linear regression.
|
I have the following setting. I have n Hermitian Positive Semidefinite (HPSD) matrices, and a metric induced by a matrix norm. I am primarily interested in the Frobenius norm and the operator norm. I want to extract the principal "principal component" for this set of observations, i.e., a 1-dimensional subspace in HPSD... |
When trying to estimate the number of sampling units with an attribute, is there a good algebraic way to aggregate over propensity scores for that attribute which each have their own error? For example, when the propensity scores may be calculated with varying amounts of information from each sampling unit and each has... |
Here is a look at my data. We asked the same respondents (n=~400) to provide us with their current and future consumption as a proportion of total expenditure. Plotted here are the mean proportions of total expenditure for each category for "Now" and "Later", respectively current and future.
What I'm looking for is a... |
I'm taking a graduate course in regression analysis and I'm suck on a particular homework question that should be very simple to me!
I have the following model:
E(y) = B0 + B1x1 + B2x2 + B3x3 + B4x1x3 + B5x2x3
x3 is coded as 1 if "smoker" and 0 if "non-smoker".
Therefore the regression equations are:
x3 = 1: E(y) = (B... |
Does anybody have a good example for Time Series Forecasting/smoothing using Kalman Filter in R?
|
This question is a follow up to my earlier question here
and is also related, in intent, to this question.
On this wiki page probability density values from an assumed normal distribution for the training set are used to calculate a Bayesian posterior rather than actual probability values. However, if a training set i... |
I wish to analyze the following :
Predictor Variable (IV): Satisfaction of sexual needs as important (4 items scale and respond based on 4 point likert scale. Sum up to get the item score.)
Response Variable (DV): Condom usagae (2 options : never or sometime)
Questions:
Should I use binary logistic or multinomial logi... |
Is there a recommendation on the number of times that an experiment should be replicated? As many of you know, is not always possible to make many replicas. What would be the recommended minimum? Is there some references to support it?
In my particular case (animal reproduction), for reasons of seasonality, I can only ... |
I was just wondering-- is it possible/practical to apply bayes' theorem without an analytical expression for the prior, only samples?
For example, say you have sufficient draws from a posterior distribution from a previous experiment via MCMC methods, and you'd like to use that posterior as the prior for a new one. Y... |
This is related to another question I asked recently. To recap:
[I had 30 people call a number and then roll a 5 sided die. If the call matches the subsequent face then the trial is a hit, else it is a miss. Each subject completes 25 trials (rolls) and thus, each participant has a score out of 25. Since the die is a vi... |
The context of this question is within a health framework i.e. looking at one or more therapies in the treatment of a condition.
It appears that even well respected researchers confuse the terms efficacy and effectiveness, using the terms interchangeably.
How can one think of efficacy versus effectiveness in a way th... |
(1) I am looking for a package for computing the power of a matrix. If you have some good recommendation please let me know.
(2) I searched on the internet and followed what some said to install a package called "Malmig" in R but after selecting the mirror site, it failed:
In install.packages("Malmig") : package ‘Malm... |
There are some cases where I would like to correct for multiple comparisons where the null hypotheses vary.
For example, if I am performing a chi-squared test or a fisher's exact test on multiple contingency tables of different sizes, the null hypotheses vary from table to table. Can I still apply the Benjamini-Hochber... |
Does anyone know of some well written code (in Matlab or R) for reversible jump MCMC? Preferably a simple demo application to compliment papers on the subject, that would be useful in understanding the process.
|
I've got a data-set which I assume is uniformly distributed. Say I've got N=20000 samples and a suspected p=0.25. This means that I would expect each option to show up roughly 5000 times.
How do I calculate the following interval [5000 - x, 5000 + x] such that I can say with a certain confidence that the data-set is pr... |
I would like to implement the model proposed in Dynamic modeling of mean-reverting spreads (Kostas Triantafyllopoulos, Giovanni Montana).
They propose to model a time serie Y_t with the following equations:
(1) Y_t = A_t + B_t * Y_(t-1) + e_t
(2) A_t = Phi1 * A_(t-1) + nu1_t
(3) B_t = Phi2 * B_(t-1) + nu2_t
That c... |
I just discovered the comment function in R. Example:
x <- matrix(1:12, 3,4)
comment(x) <- c("This is my very important data from experiment #0234",
"Jun 5, 1998")
x
comment(x)
This is the first time I came by this function and was wondering what are common/useful uses of it.
Since it is quite difficu... |
I need to do an experiment. First let me describe present situation. The company that I work for is a cinema. It has a gaming section where people who are waiting for movies can pass time by playing games. People can pay only by using prepaid membership card. Unfortunately this gaming section is not generating enough s... |
I do have a big list of numeric values (including duplicates) and I do want to group them into ranges in order to see if how do they distribute.
Let's say there are 1000 values ranging from 0 to 2.000.000 and I do want to group them.
How can I achieve this, preferably in Excel or SQL.
|
From what you have read or heard about, which is a good book on fuzzy logic/sets/systems? I'm interested in basic of fuzzy systems, fuzzification/defuzzification, etc.
|
I am trying to use R to conduct community division within my weighted network (based from an association matrix). I tried with igraph but I encountered some problems. I usually use the program Socprog (Whitehead 2009) for my analysis, but as I would like to conduct a community division with Newman modularity (2006) on ... |
when fitting GAMM with R, I would like to know why when the smooth function is linear, the confidence interval is zero around the middle (the dotted lines are crossing each other at the middle)
|
I was wondering if there are any distributions besides the normal where the mean and variance are independent of each other (or in other words, where the variance is not a function of the mean).
|
I know that R's rpart function keeps the data it would need to implement multivariate split, but I don't know if it's actually performing multivariate splits. I've tried researching it online looking at the rpart docs, but I don't see any information that it can do it or is doing it. Anyone know for sure?
|
Let's say we are repeatedly tossing a fair coin, and we know number of heads and tails should be roughly equal. When we see a result like 10 heads and 10 tails for a total of 20 tosses, we believe the results and are inclined to believe the coin is fair.
Well when you see a result like 10000 heads and 10000 tails for a... |
A standardized Gaussian distribution on $\mathbb{R}$ can be defined by giving explicitly its density:
$$ \frac{1}{\sqrt{2\pi}}e^{-x^2/2}$$
or its characteristic function.
As recalled in this question it is also the only distribution for which the sample mean and variance are independent.
What are other surprising al... |
I believe $p[x]$ is a probability distribution, where
\begin{equation}
p[x] = \frac{1}{\pi (1+x^2)}
\end{equation}
since it's positive everywhere and integrates to 1 on $-\infty, \infty$.
The mean is 0 by symmetry, even though integrating $xp[x]$ on
$-\infty, \infty$ does not converge. This is "suspicious" since
$p... |
Why in the white test, we estimate auxiliary regression model of the squared residuals (in the original model) and not just plain residuals?
|
In "The Elements of Statistical Learning" (2nd ed), p63, the authors give the following two formulations of the ridge regression problem:
$$ \hat{\beta}^{ridge} = \underset{\beta}{\operatorname{argmin}} \left\{ \sum_{i=1}^N(y_i-\beta_0-\sum_{j=1}^p x_{ij} \beta_j)^2 + \lambda \sum_{j=1}^p \beta_j^2 \right\} $$
and
$$ \... |
I want to model the probability of a binary variable x given some predictor, d. It needs two parameters:
One parameter that sets the "break point", at which p(x=1 | d) = 0.5.
One parameter that sets the "softness", i.e. how abruptly the probability changes around the break point.
(Sorry I'm sure there's standard ter... |
[edits made in response to feedback- thanks :-) ]
Doh! More edits! Sorry!
Hello-
I am doing some rather rough and ready data collection with a survey sent out to healthcare staff using a published scale about morale and other such issues.
The only thing is that the scale is rather long with all the other things in the ... |
Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample $x_1$ from $X$ and $y_1$ from $Y$, what is the maximum likelihood estimator of the mean of $Z$?
|
It occurred to me that, while I've pieced together some ideas over the years about the differences between statistics and biostatistics, I've never heard a formal explanation. What is the distinction between these two disciplines (currently)? And why did this distinction begin in the first place?
EDIT: I've not been ... |
I have a data file in which each participant is tested many times in several blocks. The data is formatted so that each trial contains a participant id, a block number and a score. What I want to do is group the data by participant and block, then rank the scores for each group, so I can use the top 50%.
For example:
p... |
I'm looking at attempting to capture the regularity of a time series of events, one measurement per day, with a year's worth of data, and there can be at most one event a day. Say for example the day you do laundry. What I want to capture is a measurement of regularity. Capturing irregularity is straight forward: goodn... |
In our usage of R for a non-trivial data analysis and estimation project, we've been repeatedly burnt by how tolerant R is toward misspelled or missing columns in a data frame. Typical example is calculating the weighted mean of a variable MYVAR in a data frame using another variable WEIGHT for weights:
m <- weighted.m... |
We need to estimate the probability of a person getting a question right for a given content area given his history of getting questions in the same content area right in the past. We would also presumably have records on how others have done on this question and in this content area.
Is there a good way or ways of do... |
Could anybody provide me a latest material related to Cross validation especially R package?
|
In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
|
Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample $x_1$ from $X$ and $y_1$ from $Y$, what is the minimum mean squared error estimator of the mean of $Z$? Is there a biased... |
FULL DISCLOSURE: This is homework.
I have been provided with a small data set (n=21) the data are messy, looking at it in a scatterplot matrix provides me with little to no insight. I've been provided with 8 variables that are metrics created from a longditudinal study (BI, CONS, CL, CR, ..., VOBI). The other measureme... |
It is helpful to study the data analysis code of experts.
I've recently been perusing github and there are a number of people sharing data analysis code there. This includes a few R Packages (which of course are available directly from CRAN), but also several examples of reproducible research, particularly using R (see... |
Way back when, I used to work in finance, and I remember helping a coworker use some kind of block bootstrap. (I believe the application was: we had weekly data on some financial indicator X, along with weekly data on some stock, and we wanted to measure how well X could be used to predict the stock's movements. And I ... |
so we have a0:
>a0[1,1:2]
l11 l12
-0.921 0.389593
Then;
> is.numeric(a0[1,1:2])
[1] FALSE
Ok, the text file containing them is a bit of a mess. Then:
> as.numeric(a0[1,1:2])
[1] 131 3
I know there was a trick to solve that. I just can't remember what it was...
EDIT: sample file:
-0.921 0.389593 0.9... |
I am collecting longitudinal data using for 4 time waves. Although the survey is administrated to the same population, different individuals may decide to complete it at each time point. As a result there are a number of individuals that only completed it once, others that completed it twice, some that completed it th... |
A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, state, whatever). Populations are usually not uniformly distributed within their polygons, however. Dasymetric mapping... |
The standard sum of squares as I know it is:
$$
\sum(X-m)^2
$$
where $m$ is the mean. I ran into a different one which can be written two ways:
$$
\sum(X^2) - \frac{(\sum X)^2}{n} = \sum(X^2) - m\sum X
$$
I believe the latter is called the "correction term for the mean" (e.g. here). My algebra seems to be inadequate t... |
I am looking for social network datasets (twitter, friendfeed, facebook, lastfm, etc.) for classification tasks, preferably in arff format.
My searches via UCI and Google weren't successful so far... any suggestions?
|
Suppose I have a set $\mathcal{S}$ of $N$ distinct items. Now consider the set $\mathcal{P}$ of all possible pairs that I can draw from $S$. Naturally, $|\mathcal{P}| = \binom{N}{2}$. Now when I draw $k$ items (pairs) from $\mathcal{P}$ with a uniform distribution, what is the expected number of distinct items from $S$... |
Are there any decent tools for writing/designing questionnaires before providing to programmers? Currently Microsoft Word is being used and tracking changes and keeping it standardized has become a headache.
Update: I think I'm being a little misunderstood here. Here's a scenario: A client speaks to a statistician/expe... |
I do a bunch of real estate reporting and the median price is often reported, particularly by the NAR (National Association Of Realtors). As best I can tell, they only get the medians of real estate prices from each area. My question is, how should the national median be calculated, given the data restrictions? As a m... |
I am a student, working with a team on a large-scale ecological experiment. We want to analyze survival data which has been derived from an experimental design with some pseudo-replication. This pseudo-replication was not discovered, unfortunately, until the middle of the experiment, at which point the design could not... |
Context:
In response to an earlier question about reproducible research Jake wrote
One problem we discovered when
creating our JASA archive was that
versions and defaults of CRAN packages
changed. So, in that archive, we also
include the versions of the packages
that we used. The vignette based
system will... |
Is there a way to type in a regression formula in SPSS in the same manner as R, with weights?
For example, in R, I would write something like:
lm(y ~ B1 + B2 + B1*B2, data=df, weights=x)
How would I go about recreating this in SPSS/PASW?
|
For chi squared distribution, how would I find quantiles for the following three cases:
A) $P(X^2> X^2_{\alpha})=0.01$ when $v = 21$
B) $P(X^2 < X^2_{\alpha})=0.95$ when $v =6$
C) $P(X^2_{\alpha} < X^2 <23.209) = 0.015$ when $v = 10$
Here $X^2_{\alpha}$ is the $\alpha$-quantile of the $\chi^2_{v}$ distribution.
|
I've created a model (cue ominous music) in R based on previous months data using lm(). Now, I would like to see how well it predicts the current months data.
For example, my model predicts sales figures. I have figures for January, February and March. My model is based on figures from January and February and I would... |
Or more specifically, why would the index of a dataframe not be in ascending numerical order?
When I display the dataframe, the first row has column names, the data begins on second row, but the leftmost column (which doesn't have a header), is not in order, instead it shows as:
2
1
4
6
5
3
|
As described in a few of my previous questions (here and there), I am interested in deriving summary statistics from statistics reported in the literature.
I would very much appreciate any advice into the validity or errors found in the following calculations.
To solve for $MSE$ given $F$, $df_{\text{group}}$, and $S... |
Consider the following graph:
x <- 1:100
y1 <- rnorm(100)
y2 <- rnorm(100)+100
par(mar=c(5,5,5,5))
plot(x,y1,pch=0,type="b",col="red",yaxt="n",ylim=c(-8,2),ylab="")
axis(side=2, at=c(-2,0,2))
mtext("red line", side = 2, line=2.5, at=0)
par(new=T)
plot(x,y2,pch=1,type="b",col="blue",yaxt="n",ylim=c(98,108), ylab="")
... |
I'm using the following code to insert vertical lines in a timeseries plot:
abline(v=as.Date("2007-09-19"),col="red",lty=2)
abline(v=as.Date("2008-03-10"),col="red",lty=2)
abline(v=as.Date("2008-04-28"),col="red",lty=2)
abline(v=as.Date("2009-08-07"),col="red",lty=2)
But I would rather prefer a small triangle pointing... |
Consider the following code:
require(zoo)
data <- read.csv(file="summary.csv",sep=",",head=TRUE)
data = zoo(data$compressed, as.Date(data$date))
data <- aggregate(data, identity, tail, 1)
days = seq(start(data), end(data), "day")
data2 = na.locf(merge(data, zoo(,days)))
par(bty = 'n')
plot(data2,xlab='',ylab='entropy ... |
They all seem to represent random variables by the nodes and (in)dependence via the (possibly directed) edges. I'm esp interested in a bayesian's point-of-view.
|
Context:
I've recently adopted version control as part of my data analysis work (finally I may hear you saying: see my earlier question on SO). This prompted me to think more about repositories and the directory structure I use for my projects.
My typical research work involves one or more studies (i.e., data that I h... |
I've been thinking recently about conventions for figure width in data analysis reports that lead to PDFs (e.g., in A4 or Letter size). My usual context is R, Sweave, and LaTeX.
The default figure width in Sweave is 80% of the text-width (i.e., the width of a paragraph of text).
\setkeys{Gin}{width=0.80\textwidth}
Que... |
Let $G = (V,E)$ be a directed acyclic graph.
Let $i \rightarrow j$ be an edge such that the parents of $j$ are exactly:
the parents of $i$,
and $i$.
Let $L\left(G \right)$ be the set defined by {a vertex and its parents, for all vertices in $G$}
Let $G' = (V,F)$ where $F$ is $E$ with $j \rightarrow i$ instead ... |
I have fit a linear model using the lm function in R...
model <- lm(trans.baseline.CD4 ~ hiv$Julian.Date)
... and I would like to assess the quality of the model's fit. Is there a function in R that will do this? Alternatively, I found a formula for goodness-of-fit involving the sum of squared residuals given the null... |
Can you give me examples of machine learning algorithms which learn from the statistical properties of the dataset not the individual observations itself i.e. employ the statistical query model?
|
Lets say we have $T$ tags and $N$ articles and lets say that for each tag $t_{i}$ we know that it has tagged $n_{i}$ articles. Meaning that, frequency($t_{i}$)=$n_{i}$.
Given the above information how could I compute the probability P($t_{i}$ to tag a new article) or more generally how could I go about scoring the "imp... |
Is it possible to have a (multiple) regression equation with two or more dependent variables? Sure, you could run two separate regression equations, one for each DV, but that doesn't seem like it would capture any relationship between the two DVs?
|
I plotted a set of about 200,000 points and got a triangular shaped region. The shape is roughly like the triangle made by the points $(1,0)$, $(0,1)$ and $(0,0)$. My points have the property that if $(a,b)$ is a member of the set, then $(b,a)$ is also a member. I wanted to do a regression on the variable associated... |
The following code:
require(zoo)
data <- read.csv(file="summary.csv",sep=",",head=TRUE)
cum = zoo(data$dcomp, as.Date(data$date))
data = zoo(data$compressed, as.Date(data$date))
data <- aggregate(data, identity, tail, 1)
cum <- aggregate(cum, identity, sum, 1)
days = seq(start(data), end(data), "day")
data2 = na.locf... |
I am exploring the use of the survreg function in R to analyze my current experiment.
Does anyone know what the "Value" column in the output of the function stands for?
|
I have been trying to discern what exactly the "coef" and "(exp)coef" output of coxph signify. It seems that the "(exp)coef" are comparisons of the first variable in the model according to the group assigned in the command.
How does the coxph function arrive at the values for "coef" and "(exp)coef"?
Additionally, how ... |
Yesterday, I ran a repeated-measures ANCOVA. The purpose was to determine the usability of two computer systems, call them 1 and 2. Each subject completed three (conceptually different) tasks, call them A B and C, on each system. (The covariate was whether the subject had prior experience with the current system, sy... |
I have kinda puzzled when I heard from the other about the calculation of incidence rate
From Kenneth Rothman's Modern Epidemiology, the incidence rate is calculated as number of cases in a fix period of time divided by person-time at risk at that period of time, which mean if the patient has the disease in the middle ... |
After running a study based on interactive genetic algorithms, I have a univariate data file containing multiple participants each doing multiple generations (blocks) of multiple trials.
Is there an established approach used to analyse this?
I've looked at using a grand mean on each of the component variables. I've als... |
I am fitting a linear model in R using glmnet. The original (non-regularized) model was fitted using lm and did not have a constant term (i.e. it was in the form lm(y~0+x1+x2,data)).
glmnet takes a matrix of predictors and a vector of responses. I've been reading glmnet documentation, and can find no mention of the con... |
Please provide R code which allows one to conduct a between-subjects ANOVA with -3, -1, 1, 3 contrasts. I understand there is a debate regarding the appropriate Sum of Squares (SS) type for such an analysis. However, as the default type of SS used in SAS and SPSS (Type III) is considered the standard in my area. Thu... |
I'm a grad student in psychology, and as I pursue more and more independent studies in statistics, I am increasingly amazed by the inadequacy of my formal training. Both personal and second hand experience suggests that the paucity of statistical rigor in undergraduate and graduate training is rather ubiquitous within ... |
Having the Transfer Function of a discrete system as such:
$$H(z) = \frac{0.8}{z(z-0.8)}$$
I am asked to find the Steady State Gain of the system.
I have the solution and it simply states:
Steady State Gain:
$$H(1) = \frac{0.8}{1-0.8} = 4$$
I have no idea why this is the case, and the book, the slides, the solutio... |
For a university paper, I have to compare whether two program versions are statistically significantly different. The comparison in terms of runtime performance is straightforward -- I determine whether the confidence intervals for the two sets of measurements overlap. However, in the case of memory footprint, I have n... |
It is known that belief propagation gives exact result on trees, are there interesting examples when Generalized Belief Propagation is exact? (edit junction tree is not interesting because it is exactly solvable without GBP)
On the surface, Belief Propagation passes messages between cliques and separators, whereas GBP ... |
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