I have process parameter data from semiconductor manufacturing.and requirement is to suggest what could be the best parameter adjustment to be made to process parameter to get better yield ie best path for high yield. what machine learning /Statistical models best suits this requirement
Note:I have thought of using decision tree which can give us best path for high yield.
Would like to know it any other methods that can be more efficient
data is like
lotno x1 x2 x3 x4 x5 yield(%)
<95% yield is considered as 0 and >95% as 1
I'm not really sure of the question here, but as a former semiconductor process engineer, here is how I look at the yield improvement approach - perspective.
Process Development.
DOE: Typically, I would run structured DOEs to understand my process (#4). I would first identify "potential" 'factors', and run various "screening" experiments to identify statistical significance. With the goal basically here to identify the most statistically significant (and for that matter, least significant) factors. So these are inherently simple experiments, low # of "levels" which don't target understanding of the curvature of the response surface, they just look for magnitude change of response vs factor. Generally, I am most concerned with 'Process' factors, but it is important to recognize that the influence of variable inputs can come from more than just "machine knobs' as example. Variable can arise from 1) People, 2) Environment (moisture, temp, etc), 3) consumables (used in the process), 4) Equipment (is 40 psi on this tool really 40 psi and the same as 40 psi on a different tool) 4) Process variable settings.
With the most statistically significant factors, I would run more elaborate DOE using the major factors and analyze this data to develop a model. There are generally more 'levels' used here to allow for curvature insight of the response surface via the analysis. There are many types of well known standard experimental design structures here. And there is software such as JMP that is specifically set up to do this analysis.
From here, the idea would be to generate a model in the form of Response = F (Factors). That allows you to essentially optimize the response based upon these factors where the response is a reflection of your yield criteria.
From here, the engineer would typically execute confirmation runs with optimized factors to confirm optimized response.
Note that the software analysis typically allows for the engineer to illuminate any run order dependence. The execution of the DOE is typically performed in a randomized cell fashion. (Each 'cell' is a set of conditions for the experiment). Similarly the experiments include some level of repetition to gauge 'repeatability' of the 'system'. This inclusion can be explicit (run the same cell twice), but there is also some level of repeatability inherent in the design as well since you are running multiple cells, albeit at difference settings. But generally, the experiment includes explicitly repeated cells.
And finally there is the concept of manufacturability, which includes constraints of time, cost, physical limits, equipment capability, etc. (The ideal process works great, but it takes 10 years, costs 1 million dollars and requires projected settings outsides the capability of the tool.)
Since you have manufacturing data, hopefully, you have the data that captures the other types of factors as well (1,2,3), so you should specifically analyze the data to try to identify such effects. This is typically done as A vs B comparisons. Person A vs B, Tool A vs B, Consumable A vs B, Consumable lot A vs B, Summer vs Winter, etc.
Basically, there are all sorts of comparisons you could envision here and check for statistically differences across two sets of populations.
A comment on response: What is the yield criteria? You should know this in order to formulate the model. For semiconductors, we have both line yield (process yield) but there is also device yield. I assume for your work, you are primarily concerned with line yield. So minimizing variability in the factors (from 1,2,3,4) to achieve the desired response (target response(s) with minimal variability) is the primary goal.
APC (Advanced Process Control).
In many cases, there is significant trending that results from whatever reason; crappy tool control (the tool heats up), crappy consumable (the target material wears, the polishing pad wears, the chemical bath gets loaded, whatever), and so the idea here is how to adjust the next batch/lot/wafer based upon the history of what came prior. Either improve the manufacturing to avoid/minimize this trending (run order dependence) or adjust process to accommodate it to achieve the desired response.
Time for lunch, hope this helps...if you post on the specific process module type, and even equipment and consumables, I might be able to provide more insight.
Related
I'm interested in replicating "hierachies" of data say similar to addresses.
Area
District
Sector
Unit
but you may have different pieces of data associated to each layer, so you may know the area of Sectors, but not of units, and you may know the population of a unit, basically its not a homogenious tree.
I know little about replication of data except brushing Brewers theorem/CAP, and some naive intuition about what eventual consistency is.
I'm looking for SIMPLE mechanisms to replicate this data from an ACID RDB, into other ACID RDBs, systemically the system needs to eventually converge, and obviously each RDB will enforce its own local consistent view, but any 2 nodes may not match at any given time (except 'eventually').
The simplest way to approach this is to simple store all the data in a single message from some designated leader and distribute it...like an overnight dump and load process, but thats too big.
So the next simplest thing (I thought) was if something inside an area changes, I can export the complete set of data inside an area, and load it into the nodes, thats still quite a coarse algorithm.
The next step was if, say an 'object' at any level changed, was to send all the data in the path to that 'object', i.e. if something in a sector is amended, you would send the data associated to the sector, its parent the district, and its parent the sector (with some sort of version stamp and lets say last update wins)....what i wanted to do was to ensure that any replication 'update' was guaranteed to succeed (so it needs the whole path, which potentially would be created if it didn't exist).
then i stumbled on CRDTs and thought....ah...I'm reinventing the wheel here, and the algorithms are allegedly easy in principle, but tricky to get correct in practice
are there standards accepted patterns to do this sort of thing?
In my use case the hierarchies are quite shallow, and there is only a single designated leader (at this time), I'm quite attracted to state based CRDTs because then I can ignore ordering.
Simplicity is the key requirement.
Actually it appears I've reinvented (in a very crude naive way) the SHELF algorithm.
I'll write some code and see if I can get it to work, and try to understand whats going on.
I have X amount of cores doing unique work in parallel, however, their output needs to be printed in order.
Object {
Data data
int order
}
I've tried putting the objects in a min heap after they're done with their parallel work, however, even that is too much of a bottleneck.
Is there any way I could have work done in parallel and guarantee the print order? Is there a known term for my problem? Have others encountered it before?
Is there any way I could have work done in parallel and guarantee the print order?
Needless to say, we design parallelized routines with focus on an efficiency, but not constraining the order of the calculations. The printing of the results at the end, when everything is done, should dictate the ordering. In fact, parallel routines often do calculations in such a way that they’re conspicuously not in order (e.g., striding on each thread) to minimize thread and synchronization overhead.
The only question is how you structure the results to allow efficient storage and efficient, ordered retrieval. I often just use a mutable buffer or a pre-populated array. It’s very efficient in terms of both storage and retrieval. Or you can use a dictionary, too. It depends upon the nature of your Data. But I’d avoid the order property pattern in your result Object.
Just make sure you’re using optimized build if using standard Swift collections, as this can have a material impact on performance.
Q : Is there a known term for my problem?
Yes, there is. A con·tra·dic·tion:
Definition of contradiction…2a : a proposition, statement, or phrase that asserts or implies both the truth and falsity of something// … both parts of a contradiction cannot possibly be true …— Thomas Hobbes
2b : a statement or phrase whose parts contradict each other// a round square is a contradiction in terms
3a : logical incongruity
3b : a situation in which inherent factors, actions, or propositions are inconsistent or contrary to one anothersource: Merriam-Webster
Computer science, having borrowed the terms { PARALLEL | SERIAL | CONCURRENT } from the theory of systems, respects the distinctive ( and never overlapping ) properties of each such class of operations, where:
[PARALLEL] orchestration of units-of-work implies, that any and every work-unit: a) starts and b) gets executed and c) gets finished at the same time, i.e. all get into/out-of [PARALLEL]-section at once and being elaborated at the very same time, not otherwise.
[SERIAL] orchestration of units-of-work implies, that all work-units be processed in a one, static, known, particular order, starting work-unit(s) in such an order, just a (known)-next one after previous one has finished its work - i.e. one-after-another, not otherwise.
[CONCURRENT] orchestration of units-of-work permits to start more than one unit-of-work, if resources and system conditions permit (scheduler priorities obeyed), resulting in unknown order of execution and unknown time of completion, as both the former and the latter depend on unknown externalities (system conditions and (non)-availability of resources, that are/will be needed for a particular work-unit elaboration)
Whereas there is an a-priori known, inherently embedded sense of an ORDER in [SERIAL]-type of processing ( as it was already pre-wired into the units-of-work processing-orchestration-code ), it has no such meaning in either [CONCURRENT], where opportunistic scheduling makes a wished-to-have order an undeterministically random result from the system states, skewed by the coincidence of all other externalities, and the same wished-to-have order is principally singular value in true [PARALLEL] by definition, as all start/execute/finish at-the-same-time - so all units-of-work being executed in [PARALLEL] fashion have no other chance, but be both 1st and last at the same time.
Q : Is there any way I could have work done in parallel and guarantee the print order?
No, unless you intentionally or unknowingly violate the [PARALLEL] orchestration rules and re-enter a re-[SERIAL]-iser logic into the work-units, so as to imperatively enforce any such wished-to-have ordering, that is not known, the less natural for the originally [PARALLEL] work-units' orchestration ( as is a common practice in python - using a GIL-monopolist indoctrinated stepping - as an example of such step )
Q : Have others encountered it before?
Yes. Since 2011, each and every semester this or similar questions reappear here, on Stack Overflow at growing amounts every year.
How do people deal with problems where the legal actions in different states are different? In my case I have about 10 actions total, the legal actions are not overlapping, meaning that in certain states, the same 3 states are always legal, and those states are never legal in other types of states.
I'm also interested in see if the solutions would be different if the legal actions were overlapping.
For Q learning (where my network gives me the values for state/action pairs), I was thinking maybe I could just be careful about which Q value to choose when I'm constructing the target value. (ie instead of choosing the max, I choose the max among legal actions...)
For Policy-Gradient type of methods I'm less sure of what the appropriate setup is. Is it okay to just mask the output layer when computing the loss?
There are two closely related works in recent two years:
[1] Boutilier, Craig, et al. "Planning and learning with stochastic action sets." arXiv preprint arXiv:1805.02363 (2018).
[2] Chandak, Yash, et al. "Reinforcement Learning When All Actions Are Not Always Available." AAAI. 2020.
Currently this problem seems to not have one, universal and straight-forward answer. Maybe because it is not that of an issue?
Your suggestion of choosing the best Q value for legal actions is actually one of the proposed ways to handle this. For policy gradients methods you can achieve similar result by masking the illegal actions and properly scaling up the probabilities of the other actions.
Other approach would be giving negative rewards for choosing an illegal action - or ignoring the choice and not making any change in the environment, returning the same reward as before. For one of my personal experiences (Q Learning method) I've chosen the latter and the agent learned what he has to learn, but he was using the illegal actions as a 'no action' action from time to time. It wasn't really a problem for me, but negative rewards would probably eliminate this behaviour.
As you see, these solutions don't change or differ when the actions are 'overlapping'.
Answering what you've asked in the comments - I don't believe you can train the agent in described conditions without him learning the legal/illegal actions rules. This would need, for example, something like separate networks for each set of legal actions and doesn't sound like the best idea (especially if there are lots of possible legal action sets).
But is the learning of these rules hard?
You have to answer some questions yourself - is the condition, that makes the action illegal, hard to express/articulate? It is, of course, environment-specific, but I would say that it is not that hard to express most of the time and agents just learn them during training. If it is hard, does your environment provide enough information about the state?
Not sure if I understand your question correctly, but if you mean that in certain states some actions are impossible then you simply reflect it in the reward function (big negative value). You can even decide to end the episode if it is not clear what state would the illegal action result in. The agent should then learn that those actions are not desirable in the specific states.
In exploration mode, the agent might still choose to take the illegal actions. However, in exploitation mode it should avoid them.
I recently built a DDQ agent for connect-four and had to address this. Whenever a column was chosen that was already full with tokens, I set the reward equivalent to losing the game. This was -100 in my case and it worked well.
In connect four, allowing an illegal move (effectively skipping a turn) can in some cases be advantageous for the player. This is why I set the reward equivalent to losing and not a smaller negative number.
So if you set the negative reward greater than losing, you'll have to consider in your domain what are the implications of allowing illegal moves to happen in exploration.
If a technical indicator works very slow, and I wish to include it in an EA ( using iCustom() ), is there a some "wrapper" that could cache the indicator results to a file based on the particular indicator inputs?
This way I could get a better speed next time when I backtest it using the same set of parameters, since the "wrapper" could read the result from file rather than recalculate the result from the indicator.
I heard that some developers did that for their needs in order to speed up backtesting, but as far as i know, there's no publicly available solution.
If I had to solve this problem, I would create a class with two fields (datetime and indicator value, or N buffers of the indicator), and a collection class similar to CArrayObj.mqh but with an option to apply binary search, or to start looking for element from a specific index, not from the very beginning of the array.
Recent MT4 Builds added VERY restrictive conditions for Indicators
In early years of MT4, this was not so cruel as it is these days.
FACT#1: fileIO is 10.000x ~ 100.000x slower than memIO:
This means, there is no benefit from "pre-caching" values to disk.
FACT#2: Processing Performance has HARD CEILING:
All, yes ALL, Custom Indicators, that are being used in MetaTrader4 Terminal ( be it directly in GUI, or indirectly, via Template(s) or called via iCustom() calls & in Strategy Tester via .tpl + iCustom() ) ALL THESE SHARE A SINGLE THREAD ...
FACT#3: Strategy Tester has the most demanding needs for speed:
Thus - eliminate all, indeed ALL, non-core indicators from tester.tpl template and save it as "blank", to avoid any part of such non-core processing.
Next, re-design the Custom Indicator, where possible, so as to avoid any CPU-ops & MEM-allocation(s), that are not necessary.
I remember a Custom Indicatore designs with indeed deep-convolutions, which could have been re-engineered so as to keep just a triangular sparse-matrix with necessary updates, that has increased the speed of Indicator processing more than 10.000x, so code-revision is the way.
So, rather run a separate MetaTrader4 Terminal, just for BackTesting, than having to wait for many hours just due to un-compressible nature of numerical processing under a traffic-jam congestion in the shared use of the CustomIndicator-solo-Thread that none scheduling could improve.
FACT#4: O/S can increase a process priority:
Having got to the Devil's zone, it is a common practice to spin-up the PRIO for the StrategyTester MT4, up to the "RealTime PRIO" in the O/S tools.
One may even additionally "lock" this MT4-process onto a certain CPU-core(s) and setup all other processes with adjacent CPU-core-AFFINITY, so that these two distinct groups of processes do not jump one to the other group's CPU-core(s). Hard, but if squeezing the performance to the bleeding edge, this is a must.
I was not able to find why we should have a global innovation number for every new connection gene in NEAT.
From my little knowledge of NEAT, every innovation number corresponds directly with an node_in, node_out pair, so, why not only use this pair of ids instead of the innovation number? Which new information there is in this innovation number? chronology?
Update
Is it an algorithm optimization?
Note: this more of an extended comment than an answer.
You encountered a problem I also just encountered whilst developing a NEAT version for javascript. The original paper published in ~2002 is very unclear.
The original paper contains the following:
Whenever a new
gene appears (through structural mutation), a global innovation number is incremented
and assigned to that gene. The innovation numbers thus represent a chronology of the
appearance of every gene in the system. [..] ; innovation numbers are never changed. Thus, the historical origin of every
gene in the system is known throughout evolution.
But the paper is very unclear about the following case, say we have two ; 'identical' (same structure) networks:
The networks above were initial networks; the networks have the same innovation ID, namely [0, 1]. So now the networks randomly mutate an extra connection.
Boom! By chance, they mutated to the same new structure. However, the connection ID's are completely different, namely [0, 2, 3] for parent1 and [0, 4, 5] for parent2 as the ID is globally counted.
But the NEAT algorithm fails to determine that these structures are the same. When one of the parents scores higher than the other, it's not a problem. But when the parents have the same fitness, we have a problem.
Because the paper states:
In composing the offspring, genes are randomly chosen from veither parent at matching genes, whereas all excess or disjoint genes are always included from the more fit parent, or if they are equally fit, from both parents.
So if the parents are equally fit, the offspring will have connections [0, 2, 3, 4, 5]. Which means that some nodes have double connections... Removing global innovation counters, and just assign id's by looking at node_in and node_out, you avoid this problem.
So when you have equally fit parents, yes you have optimized the algorithm. But this is almost never the case.
Quite interesting: in the newer version of the paper, they actually removed that bolded line! Older version here.
By the way, you can solve this problem by instead of assigning innovation ID's, assign ID based on node_in and node_out using pairing functions. This creates quite interesting neural networks when fitness is equal:
I can't provide a detailed answer, but the innovation number enables certain functionality within the NEAT model to be optimal (like calculating the species of a gene), as well as allowing crossover between the variable length genomes. Crossover is not necessary in NEAT, but it can be done, due to the innovation number.
I got all my answers from here:
http://nn.cs.utexas.edu/downloads/papers/stanley.ec02.pdf
It's a good read
During crossover, we have to consider two genomes that share a connection between the two same nodes in their personal neural networks. How do we detect this collision without iterating both genome's connection genes over and over again for each step of crossover? Easy: if both connections being examined during crossover share an innovation number, they are connecting the same two nodes because they received that connection from the same common ancestor.
Easy Example:
If I am a genome with a specific connection gene with innovation number 'i', my children that take gene 'i' from me may eventually cross over with each other in 100 generations. We have to detect when these two evolved versions (alleles) of my gene 'i' are in collision to prevent taking both. Taking two of the same gene would cause the phenotype to probably loop and crash, killing the genotype.
When I created my first implementation of NEAT I thought the same... why would you keep a innovation number tracker...? and why would you use it only for one generation? Wouldn't be better to not keep it at all and use a key value par with the nodes connected?
Now that I am implementing my third revision I can see what Kenneth Stanley tried to do with them and why he wanted to keep them only for one generation.
When a connection is created, it will start its optimization in that moment. It marks its origin. If the same connection pops out in another generation, that will start its optimization then. Generation numbers try to separate the ones which come from a common ancestor, so the ones that have been optimized for many generations are not put side to side that one that was just generated. If a same connection is found in two genomes, that means that that gene comes from the same origin and thus, can be aligned.
Imagine then that you have your generation champion. Some of their genes will have 50 percent chance to be lost due that the aligned genes are treated equally.
What is better...? I haven't seen any experiments comparing the two approaches.
Kenneth Stanley also addressed this issue in the NEAT users page: https://www.cs.ucf.edu/~kstanley/neat.html
Should a record of innovations be kept around forever, or only for the current
generation?
In my implementation of NEAT, the record is only kept for a generation, but there
is nothing wrong with keeping them around forever. In fact, it may work better.
Here is the long explanation:
The reason I didn't keep the record around for the entire run in my
implementation of NEAT was because I felt that calling something the same
mutation that happened under completely different circumstances was not
intuitive. That is, it is likely that several generations down the line, the
"meaning" or contribution of the same connection relative to all the other
connections in a network is different than it would have been if it had appeared
generations ago. I used a single generation as a yardstick for this kind of
situation, although that is admittedly ad hoc.
That said, functionally speaking, I don't think there is anything wrong with
keeping innovations around forever. The main effect is to generate fewer species.
Conversely, not keeping them around leads to more species..some of them
representing the same thing but separated nonetheless. It is not currently clear
which method produces better results under what circumstances.
Note that as species diverge, calling a connection that appeared in one species a
different name than one that appeared earlier in another just increases the
incompatibility of the species. This doesn't change things much since they were
incompatible to begin with. On the other hand, if the same species adds a
connection that it added in an earlier generation, that must mean some members of
the species had not adopted that connection yet...so now it is likely that the
first "version" of that connection that starts being helpful will win out, and
the other will die away. The third case is where a connection has already been
generally adopted by a species. In that case, there can be no mutation creating
the same connection in that species since it is already taken. The main point is,
you don't really expect too many truly similar structures with different markings
to emerge, even with only keeping the record around for 1 generation.
Which way works best is a good question. If you have any interesting experimental
results on this question, please let me know.
My third revision will allow both options. I will add more information to this answer when I have results about it.