Four common bean trials were established in fields, one trial per year. We combined density, bean genotype, and fungicide to manage white mold with a factorial scheme. The experimental design was a randomized complete block with four replicates. Each trial was analyzed by a three-way ANOVA. The fixed factors were density, genotype, fungicide, and interactions. The random factor was block.
My intent is to treat each trial as a form of replication, then I would like to combine all trials together in a more concise analysis.
We don’t want to draw conclusions between trials. We want to make conclusions of in general about our treatments.
I have used the complex model with fixed and random effects like this:
y ~ DENS:GEN:FUNG + (1 | trials) + (1 | trials:block)
I would be very grateful if someone could tell me if the model is appropriate for my search.
The model:
y ~ DENS:GEN:FUNG + (1 | trials) + (1 | trials:block)
has the following features:
A fixed effect for the 3-way interaction DENS:GEN:FUNG,
Random intercepts for block varying within levels of trials
It is very rarely a good idea to fit a 3-way interaction as a fixed effect without the 2-way interactions and the main effects. See these for further discussion:
https://stats.stackexchange.com/questions/236113/are-lower-order-interactions-a-prequisite-for-three-way-interactions-in-regressi
https://stats.stackexchange.com/questions/27724/do-all-interactions-terms-need-their-individual-terms-in-regression-model
As for the random structure, then yes, based on the description, this seems to be appropriate, although you don't state how many trials there are - if this is very few then it may be better to fit trials as a fixed effect.
Related
I am having issue in getting clear concept of contrastive loss used in siamese network.
Here is pytorch formula
torch.mean((1-label) * torch.pow(euclidean_distance, 2) +
(label) * torch.pow(torch.clamp(margin - euclidean_distance, min=0.0), 2))
where margin=2.
If we convert this to equation format, it can be written as
(1-Y)*D^2 + Y* max(m-d,0)^2
Y=0, if both images are from same class
Y=1, if both images are from different class
What i think, if images are from same class the distance between embedding should decrease. and if images are from different class, the distance should increase.
I am unable to map this concept to contrastive loss.
Let say, if Y is 1 and distance value is larger, the first part become zero (1-Y), and second also become zero, because it should choose whether m-d or 0 is bigger.
So the loss is zero which does not make sense.
Can you please help me to understand this
If the distance of a negative sample is greater than the specified margin, it should be already separable from a positive sample. Therefore, there is no benefit in pushing it farther away.
For details please check this blog post, where the concept of "Equilibrium" gets explained and why the Contrastive Loss makes reaching this point easier.
I'm currently working on a Object Detection project using Matterport MaskRCNN.
As part of the job is to detect a Green leaf that crosses a white grid. Until now I have defined the annotation (Polygons) in such a way that every single leaf which crosses the net (and gives white-green-white pattern) is considered a valid annotation.
But, when changing the definition above from single-cross annotation to multi-cross (more than one leaf crossing the net at once), I started to see a serious decrease in model performance during testing phase.
This raised my question - The only difference between the two comes down to size of the annotation. So:
Which of the following is more influential on learning during MaskRCNN's training - pattern or size?
If the pattern is influential, it's better. Because the goal is to identify a crossing. Conversely, if the size of the annotation is the influencer, then that's a problem, because I don't want the model to look for multi-cross or alternatively large single-cross in the image.
P.S. - References to recommended articles that explain the subject will be welcomed
Thanks in advance
If I understand correctly the shape of the annotation becomes longer and more stretched out if going for multicross annotation.
In that case you can change the size and side ratio of the anchors that are scanning the image for objects. With default settings the model often has squarish bounding boxes. This means that very long and narrow annotations create bounding boxes with a great difference between width and height. These objects seem to be harder to segment and detect by the model.
These are the default configurations in the config.py file:
Length of square anchor side in pixels
RPN_ANCHOR_SCALES = (32, 64, 128, 256, 512)
Ratios of anchors at each cell (width/height). A value of 1 represents a square anchor, and 0.5 is a wide anchor
RPN_ANCHOR_RATIOS = [0.5, 1, 2]
You can play around with these values in inference mode and look if it gives you some better results.
I had a random question about fixed effects and I wanted to clarify this with you. Suppose a study is at the individual by state by year level where each individual is followed over time (Panel) and I am adding state fixed effects, year fixed effects as well as state by year fixed effects. Does that mean I might run into multi-collinearity problems? Also will something like this soak up all of the variability and we would not be able to get the correct coefficient estimates?
In Stata I am doing something like reg y x i.year##i.statefip [aw=population], vce(robust)
Or should I rather do something like reg y x i.year i.statefip c.year#i.statefip [aw=population], vce(robust) as in add state specific time trends.
If you have a panel dataset, it would be much better for you to xtset it first, rather than trying to use the regular reg command. If you're using FE with xtreg, then first, the state-level fixed effects are automatically generated (and you wouldn't have to mess with the syntax in the OLS -- not sure why you would be using the regular OLS in the first place if you have panel data). Then you can include your time fixed effects with i.year. At the end, just have i.statefip and i.year, because they are both categorical and not continuous. Let me know if you have any more questions.
I am creating a mouse joint and I bump across this term, what it actually means.
documentation for mouse joint:-"A mouse joint is used to make a point on a body track a specified world point. This a soft constraint with a maximum force.
* This allows the constraint to stretch and without applying huge forces."
Let's say that we have a distance joint;
b2DistanceJointDef DistJointDef;
you can achieve a spring-like effect by tuning the frequency and damping ratios.
DistJointDef.frequencyHz = 0.5f;
DistJointDef.dampingRatio = 0.5f;
FrequencyHz will determine how much the body should stretch/shrink over time.
whereas the dampingRation will determine how long the spring-like effect will last.
These principles are also applied to Mouse joints. you can modify their frequency and damping ratio to achieve a similar effect.
If I recall correctly, you can apply the soft constraints on wheel joints as well.
here is a little bit more info on the subject from Box2dManual
Softness is achieved by tuning two constants in the definition: frequency and damping ratio. Think of the frequency as the frequency of a harmonic oscillator (like a guitar string). The frequency is specified in Hertz. Typically the frequency should be less than a half the frequency of the time step. So if you are using a 60Hz time step, the frequency of the distance joint should be less than 30Hz. The reason is related to the Nyquist frequency.
The damping ratio is non-dimensional and is typically between 0 and 1, but can be larger. At 1, the damping is critical (all oscillations should vanish).
I have gone through a couple of YOLO tutorials but I am finding it some what hard to figure if the Anchor boxes for each cell the image is to be divided into is predetermined. In one of the guides I went through, The image was divided into 13x13 cells and it stated each cell predicts 5 anchor boxes(bigger than it, ok here's my first problem because it also says it would first detect what object is present in the small cell before the prediction of the boxes).
How can the small cell predict anchor boxes for an object bigger than it. Also it's said that each cell classifies before predicting its anchor boxes how can the small cell classify the right object in it without querying neighbouring cells if only a small part of the object falls within the cell
E.g. say one of the 13 cells contains only the white pocket part of a man wearing a T-shirt how can that cell classify correctly that a man is present without being linked to its neighbouring cells? with a normal CNN when trying to localize a single object I know the bounding box prediction relates to the whole image so at least I can say the network has an idea of what's going on everywhere on the image before deciding where the box should be.
PS: What I currently think of how the YOLO works is basically each cell is assigned predetermined anchor boxes with a classifier at each end before the boxes with the highest scores for each class is then selected but I am sure it doesn't add up somewhere.
UPDATE: Made a mistake with this question, it should have been about how regular bounding boxes were decided rather than anchor/prior boxes. So I am marking #craq's answer as correct because that's how anchor boxes are decided according to the YOLO v2 paper
I think there are two questions here. Firstly, the one in the title, asking where the anchors come from. Secondly, how anchors are assigned to objects. I'll try to answer both.
Anchors are determined by a k-means procedure, looking at all the bounding boxes in your dataset. If you're looking at vehicles, the ones you see from the side will have an aspect ratio of about 2:1 (width = 2*height). The ones viewed from in front will be roughly square, 1:1. If your dataset includes people, the aspect ratio might be 1:3. Foreground objects will be large, background objects will be small. The k-means routine will figure out a selection of anchors that represent your dataset. k=5 for yolov3, but there are different numbers of anchors for each YOLO version.
It's useful to have anchors that represent your dataset, because YOLO learns how to make small adjustments to the anchor boxes in order to create an accurate bounding box for your object. YOLO can learn small adjustments better/easier than large ones.
The assignment problem is trickier. As I understand it, part of the training process is for YOLO to learn which anchors to use for which object. So the "assignment" isn't deterministic like it might be for the Hungarian algorithm. Because of this, in general, multiple anchors will detect each object, and you need to do non-max-suppression afterwards in order to pick the "best" one (i.e. highest confidence).
There are a couple of points that I needed to understand before I came to grips with anchors:
Anchors can be any size, so they can extend beyond the boundaries of
the 13x13 grid cells. They have to be, in order to detect large
objects.
Anchors only enter in the final layers of YOLO. YOLO's neural network makes 13x13x5=845 predictions (assuming a 13x13 grid and 5 anchors). The predictions are interpreted as offsets to anchors from which to calculate a bounding box. (The predictions also include a confidence/objectness score and a class label.)
YOLO's loss function compares each object in the ground truth with one anchor. It picks the anchor (before any offsets) with highest IoU compared to the ground truth. Then the predictions are added as offsets to the anchor. All other anchors are designated as background.
If anchors which have been assigned to objects have high IoU, their loss is small. Anchors which have not been assigned to objects should predict background by setting confidence close to zero. The final loss function is a combination from all anchors. Since YOLO tries to minimise its overall loss function, the anchor closest to ground truth gets trained to recognise the object, and the other anchors get trained to ignore it.
The following pages helped my understanding of YOLO's anchors:
https://medium.com/#vivek.yadav/part-1-generating-anchor-boxes-for-yolo-like-network-for-vehicle-detection-using-kitti-dataset-b2fe033e5807
https://github.com/pjreddie/darknet/issues/568
I think that your statement about the number of predictions of the network could be misleading. Assuming a 13 x 13 grid and 5 anchor boxes the output of the network has, as I understand it, the following shape: 13 x 13 x 5 x (2+2+nbOfClasses)
13 x 13: the grid
x 5: the anchors
x (2+2+nbOfClasses): (x, y)-coordinates of the center of the bounding box (in the coordinate system of each cell), (h, w)-deviation of the bounding box (deviation to the prior anchor boxes) and a softmax activated class vector indicating a probability for each class.
If you want to have more information about the determination of the anchor priors you can take a look at the original paper in the arxiv: https://arxiv.org/pdf/1612.08242.pdf.