I experience big discrepancies when calculating melting temperature of RNA 7-mers with Biopython over values generated by a popular algorithm.
I tried the nearest neighbour algorithm with RNA and salt concentrations as described in a respective paper (thermodynamic table used as in paper below from: Freier et al 1986). Yet, the values largely differ (execute code below to see).
I tried all seven salt correction methods provided by Biopython, still I never get close to the values generated by siRNA design algorithm for the same 7-mers.
Can someone tell me how accurate Biopython's melting temperature nearest neighbour algorithm is? Especially for short oligomers like my 7-mers? Is there maybe something I am implementing wrong? Any suggestions?
Values derived from executing sample input:
http://sidirect2.rnai.jp/
Tm is given for the seed duplex of the guide strand: bases 2-7
Literature:
"Thermodynamic stability and Watson–Crick
base pairing in the seed duplex are major
determinants of the efficiency of the
siRNA-based off-target effect"
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2602766/pdf/gkn902.pdf
from Bio.Seq import Seq
from Bio.SeqUtils import MeltingTemp
test_list = [
('GGAUUUG', 21.5),
('CUCAUUG', 18.1),
('CAUAUUC', 8.7),
('UUUGAGU', 19.2),
('UUUUGAG', 12.2),
('GUUUCAA', 14.9),
('AGUUUCG', 19.7),
('GAAGUUU', 13.3)
]
for t in test_list:
myseq = Seq(t[0])
tm = MeltingTemp.Tm_NN(myseq, dnac1=100, Na=100, nn_table=MeltingTemp.RNA_NN1, saltcorr=7) # NN1 = Freier et al (1986)
tm = round(tm, 1) # round to one decimal
print 'BioPython Tm: ' + str(tm) + ' siDirect Tm: ' + str(t[1])
I answered the question at biology.stackexchange and Biostars. In short: It seems that siDirect calculates the Tm wrong due to using a 1000fold higher primer concentration.
Related
I've run an Interrupted Time Series Analysis using a Binomial logistic regression in R.
glm(`Subject Refused Ratio` ~ Quarter + int2 + time_since_intervention2 , df, family = "binomial"(link='logit'), weights = sub_weight)
I want to derive the coefficients and confidence intervals for each of my outcomes and am currently doing so with the margins package, with the following outcome:
summary(margins(rrfit1a))
factor AME SE z p lower upper
int2 0.0963 0.1064 0.9050 0.3654 -0.1122 0.3047
Quarter -0.0006 0.0049 -0.1162 0.9075 -0.0101 0.0089
time_since_intervention2 -0.0056 0.0209 -0.2695 0.7875 -0.0466 0.0353
These seem largely consistent with the modelled data. For example it suggests the intervention (int2) could range between a 0.11 decrease and 0.30 increase.
However, I really need to add similar coefficient values and confidence intervals for the original Intercept. I have tried to do so using simple exp(coefficients) and the confint function within the MASS package. But the outcome doesn't quite tie in with what I would anticipate seeing.
exp(coefficients(rrfit1a))
(Intercept) Quarter int2 time_since_intervention2
0.9093160 0.9977377 1.4720697 0.9776187
For context the fitted value of the model in the first observation is around 0.47, which looks correct. So I wonder whether it is just a case of me misinterpreting the above or is there something more fundamental wrong with it?
Secondly, the confint outcome is:
> confint(rrfit1a, level = 0.90)
Waiting for profiling to be done...
5 % 95 %
(Intercept) -0.38990085 0.19896064
Quarter -0.03437363 0.02981353
int2 -0.31682909 1.09669529
time_since_intervention2 -0.16144941 0.11569710
This isn't what we'd expect to see or what our plotted confidence intervals look anything like.
I have a pretrained word2vec model in pyspark and I would like to know how big is its vocabulary (and perhaps get a list of words in the vocabulary).
Is this possible? I would guess it has to be stored somewhere since it can predict for new data, but I couldn't find a clear answer in the documentation.
I tried w2v_model.getVectors().count() but the result (970) seem too small for my use case. In case it may be relevant, I'm using short-text data and my dataset has tens of millions of messages each having from 10 to 30/40 words. I am using min_count=50.
Not quite sure why you doubt the result of .getVectors().count(), which gives the desired result indeed, as shown in the documentation link you have provided yourself.
Here is the example posted there, with a vocabulary of just three (3) tokens - a, b, and c:
from pyspark.ml.feature import Word2Vec
sent = ("a b " * 100 + "a c " * 10).split(" ") # 3-token vocabulary
doc = spark.createDataFrame([(sent,), (sent,)], ["sentence"])
word2Vec = Word2Vec(vectorSize=5, seed=42, inputCol="sentence", outputCol="model")
model = word2Vec.fit(doc)
So, unsurprisingly, it is
model.getVectors().count()
# 3
and asking for the vectors themselves
model.getVectors().show()
gives
+----+--------------------+
|word| vector|
+----+--------------------+
| a|[0.09511678665876...|
| b|[-1.2028766870498...|
| c|[0.30153277516365...|
+----+--------------------+
In your case, with min_count=50, every word that appears less than 50 times in your corpus will not be represented; reducing this number will result in more vectors.
I am trying to conduct a repeated-measures mixed-effects test with lmer and lmerTest, but I am not sure if I am doing it appropriately.
I have 6 sites with 3 plots per site that have been sampled once per year for 24 consecutive years. I have several environmental and species variables, but for simplicity, let's say I have two environmental variables (depth and temperature) and two species (species 1 and species 2). I am not interested in the time variable, changes with time, or the interactions, as this system has strong wet/dry seasonality where the effects of the dry season outweigh carry over effects of species from the prior year. I do not necessarily have data for all variables and plots every year, with some plots not sampled at times.
The question is whether species2 (a predator) has any effect on populations of species1, relative to the environmental variables.
Is it appropriate to include year as its own random effect in the model, along with plot within site?
model1 <- lmer(species1 ~ depth + temperature + species2 + (1|year) + (1|site/plot), data=data)
For this particular analysis, there were 435 total observations (plot/year), but I worry that it is not appropriately conducting repeated-measures.
anova(model1)
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
depth 0.0221 0.0221 1 145.75 0.0908 0.7635
temperature 9.0213 9.0213 1 422.19 37.0429 2.596e-09 ***
species2 0.0597 0.0597 1 418.95 0.2450 0.6208
This does not seem right. Is the a better way to incorporate year, or should I include year at all?
If I exclude year, why does the DenDF for depth change so drastically?
model1 <- lmer(species1 ~ depth + temperature + species2 + (1|year) + (1|site/plot), data=data)
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
depth 2.599 2.599 1 431.77 7.1096 0.007955 **
temperature 58.788 58.788 1 432.10 160.7955 < 2.2e-16 ***
species2 0.853 0.853 1 429.62 2.3336 0.127343
summary(M1)
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: species1 ~ depth + temperature + species2 + (1 | site/plot)
Data: data
AIC BIC logLik deviance df.resid
833.4 861.9 -409.7 819.4 428
Scaled residuals:
Min 1Q Median 3Q Max
-2.20675 -0.66119 -0.07051 0.52722 2.99942
Random effects:
Groups Name Variance Std.Dev.
plot:site (Intercept) 0.0003221 0.01795
site (Intercept) 0.2051143 0.45290
Residual 0.3656072 0.60465
Number of obs: 435, groups: plot:site, 24; site, 6
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.538258 0.325072 50.071940 -1.656 0.10401
depth 0.006338 0.002377 431.768539 2.666 0.00796 **
temperature 0.391023 0.030837 432.101095 12.681 < 2e-16 ***
species2 -0.353264 0.231252 429.615226 -1.528 0.12734
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) depth temp
depth -0.316
temperature -0.467 -0.204
specie2 -0.544 0.040 0.007
I may have asked more questions than I answered, but I hope some of this is helpful.
"The question is whether species2 (a predator) has any effect on populations of species1, relative to the environmental variables."
I think when you word it this way, it is not entirely clear. Are you interested in the effect that species2 has on species1 - depending on what the environmental variables are (in other words the effect of species2 on species1 can change depending on depth or temperature? Or do you mean you would like to compare the effects of species2 on species1 to the effects of depth or temperature on species1? Or what do you mean, exactly, by "relative to the environmental variables"?
Yes, (1|year) + (1|site/plot) is a random intercept for both year and for plot within site. If you wanted a variable to be able to vary over each group (i.e. have a random slope) you would do something like (Temperature|year) + (1|site/plot) if you thought the effect of temperature on species1 might be different in different years.
Exactly how you specify the model is going to be based on your knowledge of the biological system and your knowledge of statistics. Based on the information in your question, this random effects formulation that you have suggested appears completely reasonable to me. Yes, this is allowing you to account for grouped data (grouped by each year and by each plot within site). It is possible that with only 435 observations you may have convergence issues with an overly complex model, which you may or may not have - just something to look out for.
I am not sure what you mean by "this does not seem right" - what are you expecting to see? What is missing?
I am seeing the same model twice (below), with different values as the output, is there a copy and pasting error here, or am I missing something? The values shouldn't be off with the same model structure.
model1 <- lmer(species1 ~ depth + temperature + species2 + (1|year) + (1|site/plot), data=data)
You haven't removed year in the above line, but have below this in the summary(M1) call.
My simple answer about the year question would be yes, I would include year. Every year is so different in any biological dataset I have seen that it is worth including as a random intercept at least - exactly as you have done. If the variance of the random effect mean is estimated to be zero, then this term is as if you didn't have it there in the first place. At that point you can choose to fit that random effect as a fixed effect instead if you still would like to account for the grouped nature of the data.
Also, there are lots of resources on this. Some examples:
Bolker, Benjamin M., Mollie E. Brooks, Connie J. Clark, Shane W. Geange, John R. Poulsen, M. Henry H. Stevens, and Jada-Simone S. White. "Generalized linear mixed models: a practical guide for ecology and evolution." Trends in ecology & evolution 24, no. 3 (2009): 127-135.
Harrison, Xavier A., Lynda Donaldson, Maria Eugenia Correa-Cano, Julian Evans, David N. Fisher, Cecily ED Goodwin, Beth S. Robinson, David J. Hodgson, and Richard Inger. "A brief introduction to mixed effects modelling and multi-model inference in ecology." PeerJ 6 (2018): e4794.
https://peerj.com/articles/4794/
In following code, I know that my naivebayes classifier is working correctly because it is working correctly on trainset1 but why is it not working on trainset2? I even tried it on two classifiers, one from TextBlob and other directly from nltk.
from textblob.classifiers import NaiveBayesClassifier
from textblob import TextBlob
from nltk.tokenize import word_tokenize
import nltk
trainset1 = [('I love this sandwich.', 'pos'),
('This is an amazing place!', 'pos'),
('I feel very good about these beers.', 'pos'),
('This is my best work.', 'pos'),
("What an awesome view", 'pos'),
('I do not like this restaurant', 'neg'),
('I am tired of this stuff.', 'neg'),
("I can't deal with this", 'neg'),
('He is my sworn enemy!', 'neg'),
('My boss is horrible.', 'neg')]
trainset2 = [('hide all brazil and everything plan limps to anniversary inflation plan initiallyis limping its first anniversary amid soaring prices', 'class1'),
('hello i was there and no one came', 'class2'),
('all negative terms like sad angry etc', 'class2')]
def nltk_naivebayes(trainset, test_sentence):
all_words = set(word.lower() for passage in trainset for word in word_tokenize(passage[0]))
t = [({word: (word in word_tokenize(x[0])) for word in all_words}, x[1]) for x in trainset]
classifier = nltk.NaiveBayesClassifier.train(t)
test_sent_features = {word.lower(): (word in word_tokenize(test_sentence.lower())) for word in all_words}
return classifier.classify(test_sent_features)
def textblob_naivebayes(trainset, test_sentence):
cl = NaiveBayesClassifier(trainset)
blob = TextBlob(test_sentence,classifier=cl)
return blob.classify()
test_sentence1 = "he is my horrible enemy"
test_sentence2 = "inflation soaring limps to anniversary"
print nltk_naivebayes(trainset1, test_sentence1)
print nltk_naivebayes(trainset2, test_sentence2)
print textblob_naivebayes(trainset1, test_sentence1)
print textblob_naivebayes(trainset2, test_sentence2)
Output:
neg
class2
neg
class2
Although test_sentence2 clearly belongs to class1.
I will assume your understand that you cannot expect a classifier to learn a good model with only 3 examples, and that your question is more to understand why it does that in this specific example.
The likely reason it does that is that naive bayes classifier uses a prior class probability. That is, the probability of neg vs pos, regardless of the text. In your case, 2/3 of the examples are negative, thus the prior is 66% for neg and 33% for pos. The positive words in your single positive instance are 'anniversary' and 'soaring', which are unlikely to be enough to compensate this prior class probability.
In particular, be aware that the calculation of word probabilities involve various 'smoothing' functions (for instance, it will be log10(Term Frequency + 1) in each class, not log10(Term Frequency) to prevent low frequency words to impact too much the classification results, divisions by zero, etc. Thus the probabilities for "anniversary" and "soaring" are not 0.0 for neg and 1.0 for pos, unlike what you may have expected.
I want to implement a simple SVM classifier, in the case of high-dimensional binary data (text), for which I think a simple linear SVM is best. The reason for implementing it myself is basically that I want to learn how it works, so using a library is not what I want.
The problem is that most tutorials go up to an equation that can be solved as a "quadratic problem", but they never show an actual algorithm! So could you point me either to a very simple implementation I could study, or (better) to a tutorial that goes all the way to the implementation details?
Thanks a lot!
Some pseudocode for the Sequential Minimal Optimization (SMO) method can be found in this paper by John C. Platt: Fast Training of Support Vector Machines using Sequential Minimal Optimization. There is also a Java implementation of the SMO algorithm, which is developed for research and educational purpose (SVM-JAVA).
Other commonly used methods to solve the QP optimization problem include:
constrained conjugate gradients
interior point methods
active set methods
But be aware that some math knowledge is needed to understand this things (Lagrange multipliers, Karush–Kuhn–Tucker conditions, etc.).
Are you interested in using kernels or not? Without kernels, the best way to solve these kinds of optimization problems is through various forms of stochastic gradient descent. A good version is described in http://ttic.uchicago.edu/~shai/papers/ShalevSiSr07.pdf and that has an explicit algorithm.
The explicit algorithm does not work with kernels but can be modified; however, it would be more complex, both in terms of code and runtime complexity.
Have a look at liblinear and for non linear SVM's at libsvm
The following paper "Pegasos: Primal Estimated sub-GrAdient SOlver for SVM" top of page 11 describes the Pegasos algorithm also for kernels.It can be downloaded from http://ttic.uchicago.edu/~nati/Publications/PegasosMPB.pdf
It appears to be a hybrid of coordinate descent and subgradient descent. Also, line 6 of the algorithm is wrong. In the predicate the second appearance of y_i_t should be replaced with y_j instead.
I would like to add a little supplement to the answer about original Platt's work.
There is a bit simplified version presented in Stanford Lecture Notes, but derivation of all the formulas should be found somewhere else (e.g. this random notes I found on the Internet).
If it's ok to deviate from original implementations, I can propose you my own variation of the SMO algorithm that follows.
class SVM:
def __init__(self, kernel='linear', C=10000.0, max_iter=100000, degree=3, gamma=1):
self.kernel = {'poly':lambda x,y: np.dot(x, y.T)**degree,
'rbf':lambda x,y:np.exp(-gamma*np.sum((y-x[:,np.newaxis])**2,axis=-1)),
'linear':lambda x,y: np.dot(x, y.T)}[kernel]
self.C = C
self.max_iter = max_iter
def restrict_to_square(self, t, v0, u):
t = (np.clip(v0 + t*u, 0, self.C) - v0)[1]/u[1]
return (np.clip(v0 + t*u, 0, self.C) - v0)[0]/u[0]
def fit(self, X, y):
self.X = X.copy()
self.y = y * 2 - 1
self.lambdas = np.zeros_like(self.y, dtype=float)
self.K = self.kernel(self.X, self.X) * self.y[:,np.newaxis] * self.y
for _ in range(self.max_iter):
for idxM in range(len(self.lambdas)):
idxL = np.random.randint(0, len(self.lambdas))
Q = self.K[[[idxM, idxM], [idxL, idxL]], [[idxM, idxL], [idxM, idxL]]]
v0 = self.lambdas[[idxM, idxL]]
k0 = 1 - np.sum(self.lambdas * self.K[[idxM, idxL]], axis=1)
u = np.array([-self.y[idxL], self.y[idxM]])
t_max = np.dot(k0, u) / (np.dot(np.dot(Q, u), u) + 1E-15)
self.lambdas[[idxM, idxL]] = v0 + u * self.restrict_to_square(t_max, v0, u)
idx, = np.nonzero(self.lambdas > 1E-15)
self.b = np.sum((1.0-np.sum(self.K[idx]*self.lambdas, axis=1))*self.y[idx])/len(idx)
def decision_function(self, X):
return np.sum(self.kernel(X, self.X) * self.y * self.lambdas, axis=1) + self.b
In simple cases it works not much worth than sklearn.svm.SVC, comparison shown below (I have posted code that generates these images on GitHub)
I used quite different approach to derive formulas, you may want to check my preprint on ResearchGate for details.