Can any one please explain clearly why the time of a signal is an independent variable while the amplitude is a dependent one? I referred to some results from google but i coul not figure it out.
the raw signal what ever it is measuring it is a function of time "time-domain" which means if we plotted the "time-domain" we will get one axes for the time (t), which is independent, and another axes for the Amplitude (x(t)) which is dependent variable on the time.
Note that: the independent variable "time" could be continous or discrete. Continuos means the time could be represented as intervals eg: t=(0 -> 800). while the discrete time signal could be represented as a countable set, eg: t = (1/2,5/2,/8/2).
Also, if you have a signal with the independent variable represents the TIME, then this signal is multidimensional "more than one dimention"
Strange question. Definitely more philosophical than programming-related. Here's my view.
One explanation is that a signal is a (mathematical) function of time. That means that for each time you have one and only one amplitude value. In contrast, the same amplitude value could be found at several (or none) time instants. So if you considered amplitude as independent variable and time as dependent of amplitude, the relationship wouldn't be a function. It's easier to ask something whose answer is known to be unique (amplitude obtained at a given time) than it is to ask something that might have none, one, or arbirarily many answers (time instants corresponding to a given ampitude level).
Also, psychologically we are more often interested in finding out "what the signal value is at a given instant", as opposed to knowing "at which instants a given signal value is found". For example, questions of the type "what will the weather be like tomorrow?" are more common than "on which days from now on will the weather be sunny?". So the point of view of time as independent and amplitude as dependent on time seems more natural.
The time is a universal independent variable because nothing can change the time. On multiple time instance there can be the same value of amplitude. But on two amplitudes there can not be one time. Independent variables are those which can not be changed with respect to other parameter.
Related
having a machine which sends (not regularly) its status values 0, 1, 2, we're storing it in Graphite. Now the status means:
0 - stopped
1 - working
2 - stopped by anomaly
The requested KPIs to extract are the classical ones: how much time on status 0 or 1 or 2 in a day or a week? Before reinventing the wheel, we're looking at the best way to compute those PKIs and if in Graphite (or possible other time-series solution) there are already function which deal with summing the time where the data point value is just a condition. Clearly the time intervals to sum are not stored, it's the time elapsed between a data point and the next one.
Or should the data pre-processed to compute the time intervals and then store three data sets like: status.working, status.stopped, status.alarm and for each store when the specific "event" started and how much it lasted?
There are other KPIs, for example the number of alarms in a day. Receiving two status data points in a row both indicating status "2" is actually a single alarm condition and must count as 1.
So, is there a best way to store such data without pre-processing it? It sounds to be a common pattern but (shame on us?) we have not found this topic well explored.
Thanks.
Graphite has a number of functions that could help you here. One that stands out is the summarize() function in which you can pass an aggregation method (in this case sum) and a duration in minutes/hours/days/weeks/etc), take a look here
isNonNull is another useful function: it can be used to determine the existence of a datapoint regardless of the value.
When you say that the machie reports a value 0 to indicate it has stopped - does it actually send that value or does it report nothing? This is an important detail and will have some bearing on the end result of your solution.
I am given a financial time series that is characterized by a bunch of structural breaks, i.e. the series isn't moving (literally at all), but at some points in time the series jumps up or down. Then it stays at this level for a while until the series jumps again. So the time series basically looks like a step function.
My assumption is that these breaks come from some particular exogenous variables that are in the form of dummies. So if a particular exogenous variable takes on the value 1, (I assume) it is very likely that the series jumps.
My question is how I could model this particular time series (in a uni- or multivariate sense). I guess that standard AR(MA)-models are inappropriate. I was thinking about creating two binary variables that take on the value 1 if there's an upward (downward) break and 0 otherwise. Then I would run a dynamic probit model to test the probabilities that the exogenous variables trigger a break. What do you think about this idea? Or would you have other suggestions? Please note that I don't wanna test for structural breaks but rather formulate a time series model.
Did you try ARIMAX, TAR, or STAR models?
You said that you have time series data and you think this series is influanced by some exogeneous shocks. I think you need to include exogeneous variable in your time series analysis thats where ARIMAX comes. This modela allows you to include exogeneous variable in ARIMA model.
You also said that there are(is) structural breaks. Try Treshold AutoRegressive or Smoothed Treshold AutoRegressive. I hope this helps to find more materials about that models. Here is one click here
I am trying to understand Q-Learning,
My current algorithm operates as follows:
1. A lookup table is maintained that maps a state to information about its immediate reward and utility for each action available.
2. At each state, check to see if it is contained in the lookup table and initialise it if not (With a default utility of 0).
3. Choose an action to take with a probability of:
(*ϵ* = 0>ϵ>1 - probability of taking a random action)
1-ϵ = Choosing the state-action pair with the highest utility.
ϵ = Choosing a random move.
ϵ decreases over time.
4. Update the current state's utility based on:
Q(st, at) += a[rt+1, + d.max(Q(st+1, a)) - Q(st,at)]
I am currently playing my agent against a simple heuristic player, who always takes the move that will give it the best immediate reward.
The results - The results are very poor, even after a couple hundred games, the Q-Learning agent is losing a lot more than it is winning. Furthermore, the change in win-rate is almost non-existent, especially after reaching a couple hundred games.
Am I missing something? I have implemented a couple agents:
(Rote-Learning, TD(0), TD(Lambda), Q-Learning)
But they all seem to be yielding similar, disappointing, results.
There are on the order of 10²⁰ different states in checkers, and you need to play a whole game for every update, so it will be a very, very long time until you get meaningful action values this way. Generally, you'd want a simplified state representation, like a neural network, to solve this kind of problem using reinforcement learning.
Also, a couple of caveats:
Ideally, you should update 1 value per game, because the moves in a single game are highly correlated.
You should initialize action values to small random values to avoid large policy changes from small Q updates.
I'm making an iOS dice game and one beta tester said he liked the idea that the rolls were already predetermined, as I use arc4random_uniform(6). I'm not sure if they are. So leaving aside the possibility that the code may choose the same number consecutively, would I generate a different number if I tapped the dice in 5 or 10 seconds time?
Your tester was probably thinking of the idea that software random number generators are in fact pseudo-random. Their output is not truly random as a physical process like a die roll would be: it's determined by some state that the generators hold or are given.
One simple implementation of a PRNG is a "linear congruential generator": the function rand() in the standard library uses this technique. At its core, it is a straightforward mathematical function, and each output is generated by feeding in the previous one as input. It thus takes a "seed" value, and -- this is what your tester was thinking of -- the sequence of output values that you get is completely determined by the seed value.
If you create a simple C program using rand(), you can (must, in fact) use the companion function srand() (that's "seed rand") to give the LCG a starting value. If you use a constant as the seed value: srand(4), you will get the same values from rand(), in the same order, every time.
One common way to get an arbitrary -- note, not random -- seed for rand() is to use the current time: srand(time(NULL)). If you did that, and re-seeded and generated a number fast enough that the return of time() did not change, you would indeed see the same output from rand().
This doesn't apply to arc4random(): it does not use an LCG, and it does not share this trait with rand(). It was considered* "cryptographically secure"; that is, its output is indistinguishable from true, physical randomness.
This is partly due to the fact that arc4random() re-seeds itself as you use it, and the seeding is itself based on unpredictable data gathered by the OS. The state that determines the output is entirely internal to the algorithm; as a normal user (i.e., not an attacker) you don't view, set, or otherwise interact with that state.
So no, the output of arc4random() is not reliably repeatable by you. Pseudo-random algorithms which are repeatable do exist, however, and you can certainly use them for testing.
*Wikipedia notes that weaknesses have been found in the last few years, and that it may no longer be usable for cryptography. Should be fine for your game, though, as long as there's no money at stake!
Basically, it's random. No it is not based around time. Apple has documented how this is randomized here: https://developer.apple.com/library/mac/documentation/Darwin/Reference/ManPages/man3/arc4random_uniform.3.html
I have a 2 part question regarding downsampling on OpenTSDB.
The first is I was wondering if anyone knows whether OpenTSDB takes the last end point inclusive or exclusive when it calculates downsampling, or does it count the end data point twice?
For example, if my time interval is 12:30pm-1:30pm and I get DPs every 5 min starting at 12:29:44pm and my downsample interval is summing every 10 minute block, does the system take the DPs from 12:30-12:39 and summing them, 12:40-12:49 and sum them, etc or does it take the DPs from 12:30-12:40, then from 12:40-12:50, etc. Yes, I know my data is off by 15 sec but I don't control that.
I've tried to calculate it by hand but the data I have isn't helping me. The numbers I'm calculating aren't adding up to the above, nor is it matching what the graph is showing. I don't have access to the system that's pushing numbers into OpenTSDB so I can't setup dummy data to check.
The second question is how does downsampling plot its points on the graph from my time range and downsample interval? I set downsample to sum 10 min blocks. I set my range to be 12:30pm-1:30pm. The graph shows the first point of the downsampled graph to start at 12:35pm. That makes logical sense.I change the range to be 12:24pm-1:29pm and expected the first point to start at 12:30 but the first point shown is 12:25pm.
Hopefully someone can answer these questions for me. In the meantime, I'll continue trying to find some data in my system that helps show/prove how downsampling should work.
Thanks in advance for your help.
Downsampling isn't currently working the way you expect, although since this is a reasonable and commonly made expectations, we are thinking of changing this in a later release of OpenTSDB.
You're assuming that if you ask for a "10 min sum", the data points will be summed up within each "round" (or "aligned") 10 minute block (e.g. 12:30-12:39 then 12:40-12:49 in your example), but that's not what happens. What happens is that the code will start a 10-minute block from whichever data point is the first one it finds. So if the first one is at time 12:29:44, then the code will sum all subsequent data points until 600 seconds later, meaning until 12:39:44.
Within each 600 second block, there may be a varying number of data points. Some blocks may have more data points than others. Some blocks may have unevenly spaced data points, e.g. maybe all the data points are within one second of each other at the beginning of the 600s block. So in order to decide what timestamp will result from the downsampling operation, the code uses the average timestamp of all the data points of the block.
So if all your data points are evenly spaced throughout your 600s block, the average timestamp will fall somewhere in the middle of the block. But if you have, say, all the data points are within one second of each other at the beginning of the 600s block, then the timestamp returned will reflect that by virtue of being an average. Just to be clear, the code takes an average of the timestamps regardless of what downsampling function you picked (sum, min, max, average, etc.).
If you want to experiment quickly with OpenTSDB without writing to your production system, consider setting up a single-node OpenTSDB instance. It's very easy to do as is shown in the getting started guide.