Building a high-performance GPU computing workstation for deep learning – part I

This post is cross posted to www.ai-imaging.org .  For machine learning and AI issues, please visit the new site!

With Tensorflow released to the public, the NVidia Pascal Titan X GPU, along with (relatively) cheap storage and memory, the time was right to take the leap from CPU-based computing to GPU accelerated machine learning.

My venerable Xeon W3550 8GB T3500 running a 2GB Quadro 600 was outdated. Since a DGX-1 was out of the question ($129,000), I decided to follow other pioneers building their own deep learning workstations. I could have ended up with a multi-thousand dollar doorstop – fortunately, I did not. Criteria: 1. Reasonably fast CPU 2. Current ‘Best’ NVidia GPU with large DDR5 memory 3. Multi-GPU potential 4. 32GB or more stable RAM 5. SSD for OS 6. Minimize internal bottlenecks 7. Stable & Reliable – minimize hardware bugs 8. Dual Boot Windows 10 Pro & Ubuntu 16.04LTS 9. Can run: R, Rstudio, Pycharm, Python 3.5, Tensorflow Total:$3725

Asus X99 E 10G WS Motherboard. Retail $699 A Motherboard sets the capabilities and configuration of your system. While newer Intel Skylake and Kaby Lake CPU architectures & chipsets beckon, reliability is important in a computationally intensive build, and their documented complex computation freeze bug makes me uneasy. Also, both architectures remain PCIe 3.0 at this time. Therefore, I chose the ASUS X99 motherboard. The board implements 40 PCIe 3.0 lanes which will support three 16X PCIe 3.0 cards (i.e. GPU’s) and one 8x card. The PCIe 3.0-CPU lanes are the largest bottleneck in the system, so making these 16X helps the most. It also has a 10G Ethernet jack somewhat future-proofing it as I anticipate using large datasets in the Terabyte size. It supports up to 128GB of DDR4. The previous versions of ASUS X99 WS have been well reviewed. Intel Core i7 6850K Broadwell-E CPU Socket Retail$649

Socket LGA2011-v3 on the motherboard guides the CPU choice – the sweet spot in the Broadwell-E lineup is the overclockable 3.6Ghz 6850K with 6 cores and 15MB of L3 cache, permitting 40 PCIe lanes. $359 discounted is attractive compared to the 6900K, reviewed to offer minimal to no improvement at a$600 price premium. The 6950X is $1200 more for 4 extra cores, unnecessary for our purposes. Avoid the$650 6800K – pricier and slower with less (28) lanes. A stable overclock to 4.0Ghz is easily achievable on the 6850K.

NVidia GeForce 1080Ti 11GB – EVGA FTW3 edition Retail: $800 Last year, choosing a GPU was easy – the Titan X Pascal, a 12GB 3584 CUDA-core monster. However, by spring 2017 there were two choices: The Titan Xp, with slightly faster memory speed & internal bus, and 256 more CUDA cores; and the 1080Ti, the prosumer enthusiast version of the Titan X Pascal, with 3584 cores. The 1080Ti differs in its memory architecture – 11GB DDR5 and a slightly slower, slightly narrower bandwidth vs. the Xp. The 1080Ti currently wins on price/performance. You can buy two 1080Ti’s for the price of one Titan Xp. Also, at time of purchase, Volta architecture was announced. As the PCIe bus is the bottleneck, and will remain so for a few years, batch size into DDR5 memory & CUDA cores will be where performance is gained. A 16GB DDR5 Volta processor would be a significant performance gain from a 12GB Pascal for deep learning. Conversely, 12GB Pascal to 11GB Pascal is a relative lesser performance hit. As I am later in the upgrade cycle, I’ll upgrade to the 16GB Volta and resell my 1080Ti in the future – I anticipate only taking a loss of$250 per 1080Ti on resell.

The FTW3 edition was chosen because it is a true 2-slot card (not 2.5) with better cooling than the Founder’s Edition 1080Ti. This will allow 3 to physically fit onto this motherboard.

64 GB DDR4-2666 DRAM – Corsair Vengeance low profile Retail : $600 DDR4 runs at 2133mhz unless overclocked. Attention must be paid to the size of the DRAM units to ensure they fit under the CPU cooler, which these do. From my research, DRAM speeds over 3000 lose stability. For Broadwell there’s not much evidence that speeds above 2666mhz improves performance. I chose 64GB because 1) I use R which is memory resident so the more GB the better and 2) There is a controversial rule of thumb that your RAM should equal 2x the size of your GPU memory to prevent bottlenecks. Implementing 3 1080Ti’s, 3x 11GB = 33 GB. Implementing 2 16GB Voltas would be 32GB. Samsung 1TB 960 EVO M2 NVMe SSD Retail$500

The ASUS motherboard has a fast M2 interface, which, while using PCIe lanes, does not compete for slots or lanes. The 1TB size is sufficient for probably anything I will throw at it (all apps/programs, OS’s, and frequently used data and packages. Everything else can go on other storage. I was unnecessarily concerned about SSD heat throttling – on this motherboard, the slot’s location is in a good place which allows for great airflow over it. The speed in booting up Windows 10 or Ubuntu 16.04 LTS is noticeable.

I like to control my data, so I’m still not wild about the cloud, although it is a necessity for very large data sets. So here is a large, cheap drive for on-site data storage. For an extra $260, I can Raid 1 the drive and sleep well at night. Strike FUMA CPU Cooler. Retail$60

This was actually one of the hardest decisions in building the system – would the memory will fit under the fans? The answer is a firm yes. This dual fan tower cooler was well-rated, quiet, attractive, fit properly, half the price of other options, and my overclocked CPU runs extremely cool – 35C with full fan RPM’s, average operating temperature 42C and even under a high stress test, I have difficulty getting the temperature over 58C. Notably, the fans never even get to full speed on system control.

Corsair 750 D Airflow Edition Case. Retail $250 After hearing the horror stories of water leaks, I decided at this level of build not to go with water cooling. The 750D has plenty of space (enough for a server) for air circulation, and comes installed with 3 fans – two air intake on the front and one exhaust at upper rear. It is a really nice, sturdy, large case. My front panel was defective – the grating kept falling off – so Corsair shipped me a replacement quickly and without fuss. Cougar Vortex 14” fans – Retail$20 ea.

Two extra cougar Vortex 14” fans were purchased, one as an intake fan at the bottom of the case, and one as a 2nd exhaust fan at the top of the case. These together create excellent airflow at noise levels I can barely hear. Two fans on the CPU Heat Sink plus Three Fans on the GPU plus five fans on the case plus one in the power supply = 11 fans total! More airflow at lower RPM = silence.

Windows 10 Pro USB edition Retail $199 This is a dual boot system so, there you go. Specific limitations with this system are as follows. While it will accept four GPU’s physically, the slots are limited to 16X/16X/16X/8X with the M2 drive installed which may affect performance on the 4th GPU (& therefore deep learning model training and performance). Additionally, the CPU upgrade path is limited – without going to a Xeon, the only reasonable upgrade from the 6850K’s 14,378 passmark is the 6950X, with a passmark of 20,021. In the future if more than 128GB DDR4 is required, that will be a problem with this build. Finally, inherent bandwidth limitations exist in the PCIe 3.0 protocol and aren’t easily circumvented. PCIe 3.0 throughput is 8GB/s. Compare this to NVidia’s proprietary NVlink that allows throughput of 20-25GB/s (Pascal vs. Volta). Note that current NVlink speeds will not be surpassed until PCIe5.0 is implemented at 32GB/s in 2019. NVidia’s CUDA doesn’t implement SLI, either, so at present that is not a solution. PCIe 4.0 has just been released with only IBM adopting, doubling transfer vs. 3.0, and 5.0 has been proposed, doubling yet again. However, these faster protocols may be difficult and/or expensive to implement. A 4 slot PCIe 5.0 bus will probably not be seen until into the 2020’s. This means that for now, dedicated NVlink 2.0 systems will outperform similar PCIe systems. With that said, this system approaches a best possible build considering price and reliability, and should be able to give a few years of good service, especially if the GPU’s are upgraded periodically. Precursor systems based upon the Z97 chipset are still viable for deep learning, albeit with slower speeds, and have been matched to older NVidia 8GB 1070 GPU’s which are again half the price of the 1080Ti. In part II, I will describe how I set up the system configuration for dual boot and configured deep learning with Ubuntu 16.04LTS. Surprisingly, this was far more difficult than the actual build itself, for multiple reasons I will explain & detail with the solutions. And yes, it booted up. On the first try. If you liked this post, head over to our sister site, ai-imaging.org where part 2, part 3, and part 4 of this post are located. Further Developing the Care Model – Part 3 – Data generation and code Returning to our care model that discussed in parts one and two, we can begin by defining our variables. Each sub-process variable is named for its starting sub-process and ending sub-process. We will define mean time for the sub-processes in minutes, and add a component of time variability. You will note that the variability is skewed – some shorter times exist, but disproportionately longer times are possible. This coincides with real-life: in a well-run operation, mean times may be close to lower limits – as these represent physical (occurring in the real world) processes, there may simply be a physical constraint on how quickly you can do anything! However, problems, complications and miscommunications may extend that time well beyond what we all would like it to be – for those of us who have had real-world hospital experience, does this not sound familiar? Because of this, we will choose a gamma distribution to model our processes:  $\Gamma(a) = \int_{0}^{\infty} {t^{a-1}e^{-t}dt}$ The gamma distribution is useful because it deals with continuous time data, and we can skew it through its shaping parameters Kappa ($\kappa$) and Theta ($\theta$) . We will use the function in R : rgamma(N,$\kappa$, $\theta$) to generate our distribution between zero and 1, and use a multiplier (slope) and offset (Y-intercept) to adjust the distributions along the X-axis. The gamma distribution can deal with the absolute lower time limit – I consider this a feature, not a flaw. It is generally recognized that a probability density plot (or Kernel plot) as opposed to a histogram of distributions is more accurate and less prone to distortions related to number of samples (N). A plot of these distributions looks like this: The R code to generate this distribution, graph, and our initial values dataframe is as follows: seed <- 3559 set.seed(seed,kind=NULL,normal.kind = NULL) n <- 16384 ## 2^14 number of samples then let’s initialize variables k <- c(1.9,1.9,6,1.9,3.0,3.0,3.0,3.0,3.0) theta <- c(3.8,3.8,3.0,3.8,3.0,5.0,5.0,5.0,5.0) s <- c(10,10,5,10,10,5,5,5,5,5) o <- c(4.8,10,5,5.2,10,1.6,1.8,2,2.2) prosess1 <- (rgamma(n,k[1],theta[1])*s[1])+o[1] prosess2 <- (rgamma(n,k[2],theta[2])*s[2])+o[2] prosess3 <- (rgamma(n,k[3],theta[3])*s[3])+o[3] prosess4 <- (rgamma(n,k[4],theta[4])*s[4])+o[4] prosess5 <- (rgamma(n,k[5],theta[5])*s[5])+o[5] prosess6 <- (rgamma(n,k[6],theta[6])*s[6])+o[6] prosess7 <- (rgamma(n,k[7],theta[7])*s[7])+o[7] prosess8 <- (rgamma(n,k[8],theta[8])*s[8])+o[8] prosess9 <- (rgamma(n,k[9],theta[9])*s[9])+o[9] d1 <- density(prosess1, n=16384) d2 <- density(prosess2, n=16384) d3 <- density(prosess3, n=16384) d4 <- density(prosess4, n=16384) d5 <- density(prosess5, n=16384) d6 <- density(prosess6, n=16384) d7 <- density(prosess7, n=16384) d8 <- density(prosess8, n=16384) d9 <- density(prosess9, n=16384) plot.new() plot(d9, col=”brown”, type = “n”,main=”Probability Densities”,xlab = “Process Time in minutes”, ylab=”Probability”,xlim=c(0,40), ylim=c(0,0.26)) legend(“topright”,c(“process 1″,”process 2″,”process 3″,”process 4″,”process 5″,”process 6″,”process 7″,”process 8″,”process 9”),fill=c(“brown”,”red”,”blue”,”green”,”orange”,”purple”,”chartreuse”,”darkgreen”,”pink”)) lines(d1, col=”brown”, add=TRUE) lines(d2, col=”red”, add=TRUE) lines(d3, col=”blue”, add=TRUE) lines(d4, col=”green”, add=TRUE) lines(d5, col=”orange”, add=TRUE) lines(d6, col=”purple”, add=TRUE) lines(d7, col=”chartreuse”, add=TRUE) lines(d8, col=”darkgreen”, add=TRUE) lines(d9, col=”pink”, add=TRUE) ptime <- c(d1[1],d2[1],d3[1],d4[1],d5[1],d6[1],d7[1],d8[1],d9[1]) pdens <- c(d1[2],d2[2],d3[2],d4[2],d5[2],d6[2],d7[2],d8[2],d9[2]) ptotal <- data.frame(prosess1,prosess2,prosess3,prosess4,prosess5,prosess6,prosess7,prosess8,prosess9) names(ptime) <- c(“ptime1″,”ptime2″,”ptime3″,”ptime4″,”ptime5″,”ptime6″,”ptime7″,”ptime8″,”ptime9”) names(pdens) <- c(“pdens1″,”pdens2″,”pdens3″,”pdens4″,”pdens5″,”pdens6″,”pdens7″,”pdens8″,”pdens9”) names(ptotal) <- c(“pgamma1″,”pgamma2″,”pgamma3″,”pgamma4″,”pgamma5″,”pgamma6″,”pgamma7″,”pgamma8″,”pgamma9”) pall <- data.frame(ptotal,ptime,pdens) Where the relevant term is rgamma(n,$\kappa$, $\theta$). We’ll use these distributions in our dataset. One last concept needs to be discussed: The probability of the sub-processes’ occurence. Each sub-process has a percentage chance of happening – some a 100% certainty, others a fairly low 5% of cases. This reflects the real world reality of what happens – once a test is ordered, there’s a 100% certainty of the patient showing up for the test, but not 100% of the patients will get the test. Some cancel due to contraindications, others can’t tolerate it, others refuse, etc… The percentages that are <100% reflect those probabilities and essentially are like a non-binary boolean switch applied to the beginning of the term that describes that sub-process. We’re evolving first toward a simple generalized linear equation similar to that put forward in this post. I think its going to look somewhat like this: But we’ll see how well this model fares as we develop it and compare it to some others. The x terms will likely represent the probabilities between 0 and 1.0 (100%). For a EMR based approach, we would assign a UID (medical record # plus 5-6 extra digits, helpful for encounter #’s). We will ‘disguise’ the UID by adding or subtracting a constant known only to us and then performing a mathematical operation on it. However, for our purposes here, we would not need to do that. We’ll head on to our analysis in part 4. Programming notes in R: 1. I experimented with for loops and different configurations of apply with this, and after a few weeks of experimentation, decided I really can’t improve upon the repetitive but simple code above. The issue is that the density function returns a list of 7 variables, so it is not as easy as defining a matrix, as the length of the data frame changes. I’m sure there is a way to get around this, but for the purposes of this illustration it is beyond our needs. Email me at mailto:contact@n2value.com if you have working code that does it better! 2. For the density function, the number of samples must be a power of 2. So by choosing 16384 (2^14) we meet that goal. Setting N to that number makes the data frame more symmetric. 3. In variable names above, prosess is an intentional misspelling. Why does everthing work In Vitro but not In Vivo? Once, I was bitten by the Neurosurgery bug. (Thanks, Dr. Ojemann!) Before I became a radiologist, I researched vasospasm in Sub-arachnoid Hemorrage (SAH). It was a fascinating problem, unfortunately with very real effects for those afflicted. Nimodipene and the old “triple-H” therapy were treatment mainstays. Many Neurosurgeons added their own ‘special sauce’ – the treatment du jour. For In Vitro (in the lab) experimental interventions held great promise for this terrible complication, but nearly all would fail when applied in clinical practice, In Vivo (in real life). As physicians, we look at disease and try to find a “silver bullet” which will treat that disease 100% of the time with complete efficacy and no side effects. Using Occam’s Razor, the simplest & most obvious solution is often the best. Consider a disease cured by a drug, as in figure 1. Give the drug, get the desired response. The drug functions as a key in the lock, opening up the door. This is how most carefully designed In Vitro experiments work. But take the treatment out of the laboratory, and it fails. Why? The carefully controlled lab environment is just that – controlled. You set up a simple process, and get your result. However, the In Vivo environment is not so simple – competing complex processes maintaining physiologic homeostasis, at the cellular bio-chemical level – interact with your experiment & confound the results. And the number of disease processes that involve a simple direct cure dwindle with time – the previous generations of scientists have culled those low-hanging fruit already! You are left with this: Consider three locked doors, one after the other. You can’t open the second without opening the first, and you can’t open the third without opening up the first and second. Here, we have a good therapy, which will cure the disease process , represented by opening up door #3. But the therapy cannot get to Door #3 – it’s blocked by Doors #1 and #2. Considering the second system, which more closely approximates what we find in real life, an effecacious drug or treatment exists, which can’t get to the disease-impacting pathway, because it is “locked out” by the body’s other systems. Not exhaustively: Drug elimination, enzymatic drug inactivation, or feedback pathways counteracting the drug’s effec – it works, but the body’s own homeostatic mechanisms compensate! Experimentally though, we are not taught to think of this possibility – instead preferring a single agent with identifiable treatment results. However, many of these easy one-item solutions have already been discovered. That’s why there has been a decrease in the number of novel synthetic chemical drug discoveries lately, as opposed to growth in biologics. Remember monthly new antibiotic releases? How often do you see new antibiotics now? There is a tremendous opportunity to go back and revisit compounds that have been initially discarded for reasons other than toxicity to see if there are new or synergistic effects when combined with other therapy. Randomized controlled trials would be too large and costly to perform a priori on such compounds – but using EHR data mining, cross-validated longitudinal trials could be designed from existing patient data sets, and some of these unexpected effects could be elucidated after the fact! Then a smaller, but focused, prospective study could be used to confirm the suspected hypothesis. Big data analytics has great promise in teasing out these relationships, and the same techniques can be applied to non-pharmacologic interventions and decisions in patient care throughout medicine. In fact, the answers may already be there – we just may not have recognized it! P.S. Glad to be back after a long hiatus. Life happens! What medicine can learn from Wall Street part 6 – Systems are algorithms Systems trading on Wall Street in the early days (pre 1980’s) was done by hand or by laborious computation. Systems traded off indicators – hundreds of indicators, exist but most are either trend or anti-trend. Trending indicators range from the ubiquitous and time-honored Moving Average, to the MACD, etc… Anti-trend indicators tend to be based on oscillators such as relative strength (RSI), etc. In a trending market, the moving average will do well, but it will get chopped around in a non-trending market with frequent wrong trades. The oscillator solves some of this problem, but in a strongly trending market, tends to underperform and miss the trend. Many combinations of trend and anti-trend systems were tried with little success to develop a consistent model that could handle changing market conditions from trend to anti-trend (consolidation) and back. The shift towards statistical models in the 2000’s (see Evidence-Based Technical Analysis by Aronson) provided a different way to analyze the markets with some elements of both systems. While I would argue that mean reversion has components of an anti-trend system, I’m sure I could find someone to disagree with me. The salient point is that it is a third method of evaluation which is neither purely trend or anti-trend. Finally, the machine learning algorithms that have recently become popular give a fourth method of evaluating the markets. This method is neither trend, anti-trend, or purely statistical (in the traditional sense), so it provides additional information and diversification. Combining these models through ensembling might have some very interesting results. (It also might create a severely overfitted model if not done right). Sidebar: I believe that the market trades in different ways at different times. It changes from a technical market, where predictive price indicators are accurate, to a fundamental market, driven by economic data and conditions, to a psychologic market, where ‘random’ current events and investor sentiment are the most important aspects. Trending systems tend to work well in fundamental markets, anti-trend systems work well in technical or psychologic markets, statistical (mean reversion) systems tend to work well in technical or fundamental markets, and I suspect machine learning might be the key to cracking the psychologic market. What is an example of a psychologic market? This – the S&P 500 in the fall of 2008 when the financial crisis hit its peak and we were all wondering if capitalism would survive. By the way, this is why you pay a human to manage your money, instead of just turning it over to a computer. At least for now. So why am I bringing this up? I’m delving more deeply into Queuing & operations theory these days, wondering if it would be helpful in developing an ensemble model – part supervised learning(statistics), part unsupervised (machine) learning, part Queue Theory algorithms. Because of this, I’m putting this project on hold. But it did make me think about the algorithms involved, and I had an aha! moment that is probably nothing new to Industrial Engineering types or Operations folks who are also coders. Algorithms, like an ensemble model composed of three separate models: a linear model (Supervised Learning), a machine learning model (Unsupervised learning) and a rule based models (Queueing theory), are software coded rule sets. However, the systems we put in place in physical space are really just the same thing. The policies, procedures and operational rule sets that exist in our workplace (e.g. the hospital) are hard-coded algorithms made up of flesh and blood, equipment and architecture, operating in an analogue of computer memory – the wards and departments of the hospital. If we only optimize for one value (profit, throughput, quality of care, whatever), we may miss the opportunity to create a more robust and stable model. What if we ensembled our workspaces to optimize for all parameters? The physical systems we have in place, which stem from policies, procedures, management decisions, workspace & workflow design, are a real-life representation of a complex algorithm we have created, or more accurately has grown largely organically, to serve the function of delivering care in the hospital setting. What if we looked at this system as such and then created an ensemble model to fulfill the triple (quad) aim? How powerful that would be. Systems are algorithms. Further developing the care model – part 2 – definitions We’ve gone about as far as we can go in theoretical terms with the process model. The next step is to create a training data set on which to do further experiments and get further insights about combining process and statistics. Let’s define the variables and the dataset we will be using for this project. 1. Each encounter with the entire process (all sub-processes from start to finish) requires a unique identifier (UID). A single patient could go through the process more than once, so a UID is necessary. This can be as simple as taking their MRN and adding a four digit trailing number identifying how many times through the process. 2. For each sub-process, time is measured in minutes. Using start and stop times/dates has some added benefits but is more complex to carry out, as anyone who has ever done so will recognize (non-synced internal clocks providing erroneous time/date data, especially after power outages/surges). 3. The main times are the pathway times – Sunprocess 1-2, 2-3,3-4,4-5,5-6. 1-2 Reflects the time it takes the physician to order the study and patient transport to come for the patient. 2-3 Reflects transport time from the ED to CT holding. 3-4 Reflects time of nursing evaluation of the patient’s appropriateness for CT imaging. 4-5 Reflects the time bringing the patient into the imaging room and scanning, and sending the study to the PACS system. 5-6 Reflects the time for the radiologist to react to the study being available, interpret the study, and dictate a preliminary result in a format the ED physician can use. 4. When an interaction occurs along the inner lines we need to account for these in a realistic way. The boolean variable built into the process will take care of whether the interaction is present or not. The effect of the off-pathway interaction is to lengthen the time of the main pathway sub-processes. For example: Patient arrives in CT holding and nurse identifies a creatinine of 1.9 which needs further information for contrast imaging. She phones the ED doctor (4 min) and then phones the Radiologist to approve the study based upon that information (2 min). These phone calls are part of the overall time in subprocess 3-4 for this UID. To evaluate the time process 3-4 takes without these phone calls, simply subtract the two inner processes. Or in other words, Process3-4(theoretical)=Process3-4(actual)-(Process1-3 + Process 3-5) 5. This table will represent potential times for each part of the process, chosen at random but with some basis in fact.  Process Mean Time Variability 1-2 10 minutes – 5 / +30 minutes 2-3 15 minutes – 5 / +10 minutes 3-4 15 minutes – 10 / + 15 minutes 4-5 15 minutes -5 / +30 minutes 5-6 20 minutes -10 /+40 minutes 1-3 5 minutes – 3 / +10 minutes 1-4 5 minutes – 3 / +10 minutes 1-5 5 minutes – 3 / + 10 minutes 3-5 5 minutes – 3/ + 10 minutes 3-6 5 minutes – 3/ + 10 minutes Next post, we’ll begin coding this in an R language data frame. Quick Post on Systems vs. Statistical Learning on large datasets The other day I attended a Webinar on Big Data vs. Systems Theory hosted by the MIT Systems design & management group which offers free, and usually very good, webinars. I recommend them to anyone interested in data driven management using systems and processes. The specific lecture was “Move Over, Big Data! – How Small, Simple Models can yield Big insights” given by Dr. Larson. The lecture was very good – it discussed some of the pitfalls we might be likely to fall into with large data sets, and how algorithmic evaluation can alternatively get us to the same place, but in a different way. Great points raised within the lecture were: Always consider the average as a distribution (i.e. a confidence interval) , and compare to its median to avoid some of the pitfalls of averages. Outliers are easy to dismiss as noncontributory – but when your outlier causes significant effects on your function (i.e. ‘black swans’) you’d better include it! Averages experienced by one population may be different than averages experienced by another. (a bit more sophisticated than the N=1 concept) There was a neat discussion of Queues with Little’s law cited – L=lambda W where L=time average # of customers in system, lambda is average arrival rate and W- mean time spent by customers in the queue. M/M/K queue notation cited. Dr. Larson’s Queue Inference Engine (using a poisson distribution) was reviewed. You can find some more information about the Queue inference engine here. The point was that small models are an alternative means to sassing out big data than simply using statistical regression. I’ll admit to not knowing much about queue theory and Markov chains, but I can see some interesting applications in combination with large datasets. Much along the lines of an ensemble model, but including the queue theory as part of the ensemble… Unfortunately, as Dr. Larson noted, much like in the linear models we have been approaching, serial queues or networked queues require difficult math with many terms. The question yet to be answered is – can we provide the best of both worlds? Further Development of a care model Let’s go back to our care model expanded upon in our prior post. As eluded to, once interdependencies are considered, things get complicated fast. This might not be as apparent in our four-stage ER care delivery model, but consider a larger process with six stages, and each stage being able to interact with each other. See the figure below: For this figure, this is the generalized linear model with first order single interactions: A 23 term generalized linear model is probably not going to really help anyone and is too unweildy, so something needs to be done to get to the heart of the matter and create a model which is reasonably simple and will well-approximate this process. The issue of multi-collinearity also is relevant here. So, the next step is to get the number of terms down to what matters. This would probably be best served by a shrinkage technique or a dimension reduction technique. Shrinkage: The LASSO immediately comes to mind due to its coefficient minimization as a feature that may allow variable selection dependent on lambda. A ridge regression wouldn’t apply the same parsimony to the equation, so it keeps terms which may not help us simplify. It has been pointed out to me that there is a technique called elastic net regularization which combines features of both the LASSO and ridge regression – seems worth a look. Dimension Reduction: First using Principal component analysis to identify the most important terms in the model and then utilizing Partial least squares to consider the response. At this point, we probably have gone about as far as we can on a theoretical basis, and need to proceed on a more applied basis. That will be a subject of future posts. Thanks to Flamdrag5 for clarifying my thoughts on this post. What medicine can learn from Wall Street – Part 3 – The dynamics of time This a somewhat challenging post with cross-discipline correlations, some unfamiliar terminology, and concepts. There is a payoff! You can recap part 1 and part 2 here. The crux of this discussion is time. Understanding the progression towards shorter and shorter time frames on Wall Street enables us to draw parallels and differences in medical care delivery particularly pertaining to processes and data analytics. This is relevant because some vendors tout real-time capabilities in health care data analysis. Possibly not as useful as one thinks. In trading, the best profit one is a risk-less one. A profit that occurs by simply being present, is reliable, and reproducible, and exposes the trader to no risk. Meet arbitrage. Years ago, it was possible for the same security to be trading at different prices on different exchanges as there was no central marketplace. A network of traders could execute a buy of a stock for$10 in New York, and then sell those same shares on the Los Angeles exchange for $11. If one imagines a 1000 share transaction, a$1 profit per share yields \$1000.  It was made by the head trader holding up two phones to his head and saying ‘buy’ into one and ’sell’ into the other.*   These relationships could be exploited over longer periods of time and represented an information deficit.  However, as more traders learned of them, the opportunities became harder to find as greater numbers pursued them.  This price arbitrage kept prices reasonably similar before centralized, computerized exchanges and data feeds.

As information flow increased, organizations became larger and more effective, and time frames for executing profitable arbitrages decreased.  This led traders to develop simple predictive algorithms, like Ed Seykota did, detailed in part 1.  New instruments re-opened the profit possibility for a window of time, which eventually closed.  The development of futures, options, indexes, all the way to closed exchanges (ICE, etc…) created opportunities for profit which eventually became crowded.  Since the actual arbitrages were mathematically complex (futures have an implied interest rate, options require a solution of multiple partial differential equations, and indexes require summing instantaneously hundreds of separate securities) a computational model was necessary as no individual could compute the required elements quickly enough to profit reliably.  With this realization, it was only a matter of time before automated trading (AT) happened, and evolved into high-frequency trading with its competing algorithms operating without human oversight on millisecond timeframes.

The journey from daily prices to ever shorter prices over the trading day to millisecond prices was driven by availability of good data and reliable computing which could be counted to act on those flash prices.  Once a game of location (geographical arbitrage) turned into a game of speed (competitive pressures on geographical arbitrage) turned into a game of predictive analytics (proprietary trading and trend following) turned into a more complex game of predictive analytics (statistical arbitrage) was then ultimately turned back into a game of speed and location (High frequency trading).

The following chart shows a probability analysis of an ATM straddle position on IBM.  This is an options position.  It is not important to understand the instrument, only to understand what the image shows.  For IBM, the expected variance that exists in price at one standard deviation (+/- 1 s.d.) is plotted in below.  As time (days) increases along the X axis, the expected range widens, or becomes less accurate.

Is there a similar corollary for health care?

Yes, but.

First, recognize the distinction between the simpler price-time data which exists in the markets, vs the rich, complex multivariate data in healthcare.

Second, assuming a random walk hypothesis , security price movement is unpredictable, and at best can only be calculated so that the next price will be in a range defined by a number of standard deviations according to one’s model as seen above in the picture. You cannot make this argument in healthcare.  This is because the patient’s disease is not a random walk.  Disease follows proscribed pathways and natural histories which allow us to make diagnoses and implement treatment options.

It is instructive to consider Clinical Decision Support tools.  Please note that these tools are not a substitute for expert medical advice (and my mention does not employ endorsement).  See Esagil and diagnosis pro.  If you enter “abdominal pain” into either of the algorithms, you’ll get back a list of 23 differentials (woefully incomplete) in Esagil and 739 differentials (more complete, but too many to be of help) in Diagnosis Pro.  But this is a typical presentation to a physician – a patient complains of “abdominal pain” and the differential must be narrowed.

At the onset, there is a wide differential diagnosis.  The possibility that the pain is a red herring and the patient really has some other, unsuspected, disease must be considered.  While there are a good number of diseases with a pathognomonic presentation, uncommon presentations of common diseases are more frequent than common presentations of rare diseases.

In comparison to the trading analogy above, where expected price movement is generally restricted to a quantifiable range based on the observable statistics of the security over a period of time, for a de novo presentation of a patient, this could be anything, and the range of possibilities is quite large.

Take, for example, a patient that presents to the ER complaining “I don’t feel well.”  When you question them, they tell you that they are having severe chest pain that started an hour and a half ago.  That puts you into the acute chest pain diagnostic tree.

With acute chest pain, there is a list of differentials that needs to be excluded (or ‘ruled out’), some quite serious.  A thorough history and physical is done, taking 10-30 minutes.  Initial labs are ordered (5-30 minutes if done in a rapid, in-ER test, longer if sent to the main laboratory) an EKG and CXR (chest X-ray) are done for their speed,(10 minutes for each)  and the patient is sent to CT for a CTA (CT Angiogram) to rule out a PE (Pulmonary embolism).  This is a useful test, because it will not only show the presence or absence of a clot, but will also allow a look at the lungs to exclude pneumonias, effusions, dissections, and malignancies. Estimate that the wait time for the CTA is at least 30 minutes.

The ER doctor then reviews the results (5 minutes)- troponins are negative, excluding a heart attack (MI), the CT scan eliminated PE, Pneumonia, Dissection, Pneumothorax, Effusion, malignancy in the chest.  The Chest X-Ray excludes fracture.  The normal EKG excludes arrhythmia, gross valvular disease, and pericarditis.   The main diagnoses left are GERD, Pleurisy, referred pain, and anxiety.  ER doctor goes back to the patient (10 minutes) , patient doesn’t appear anxious & no stressors, so panic attack unlikely.  No history of reflux, so GERD unlikely.  No abdominal pain component, and labs were negative, so abdominal pathologies unlikely.  Point tenderness present on the physical exam at the costochondral junction – and the patient is diagnosed with costochondritis.  The patient is then discharged with a prescription for pain control.  (30 minutes).

Ok, if you’ve stayed with me, here’s the payoff.

As we proceed down the decision tree, the number of possibilities narrows in medicine.

In comparison, price-time data – in which the range of potential prices increase as you proceed forward in time.

So, in healthcare the potential diagnosis narrows as you proceed down the x-axis of time.  Therefore, time is both one’s friend and enemy – friend as it provides for diagnostic and therapeutic interventions which establish the patient’s disease process; enemy as payment models in medicine favor making that diagnostic and treatment process as quick as possible (when a hospital inpatient).

We’ll continue this in part IV and compare it relevance to portfolio trading.

*As an aside, the phones in trading rooms had a switch on the handheld receiver – you would push them in to talk.  That way, the other party would not know that you were conducting an arbitrage!  They were often slammed down and broken by angry traders – one of the manager’s jobs was to keep a supply of extras in his desk, and they were not hard-wired but plugged in by a jack expressly for that purpose!

**Yes, for the statisticians reading this, I know that there is an implication of a gaussian distribution that may not be proven.  I would suspect the successful houses have modified for this and have instituted non-parametric models as well.  Again, this is not a trading, medical or financial advice blog.

What Big Data visualization analytics can learn from radiology

As I research on part III of the “What Healthcare can learn from Wall Street” series, which is probably going to turn in to a Part III, Part IV, and Part V, I was thinking about visualization tools in big data and how to use them to analyze large data sets rapidly (relatively) by a human (or a deep unsupervised learning type algorithm) – and it came to me that us radiologists have been doing this for years.
If you have ever watched a radiologist reading at a PACS station (a high-end computer system which displays images quickly) you will see them scroll at a blindingly fast speed through a large series of multiple anatomic images to arrive at a diagnosis or answer a specific question.  [N.B. if you haven’t, you really should – it’s quite cool!]  Stacked upon each other, these images assemble a complete anatomic picture of the area of data acquisition.

What the radiologist is doing while going over the images is comparing the expected appearance of a reference standard to that visualized image to find discrepancies.  The data set looks like THIS:

It’s important to understand that each pixel on the screen represents not a point, but a volume, called a voxel.  The reconstruction algorithms can sometimes over or under emphasize the appearance of the voxel, so the data is usually reconstructed in multiple axes.  This improves diagnostic accuracy and confidence.

Also, the voxel is not a boolean (binary) zero or one variable – it is a scalar corresponding to a grey-scale value.

So, in data science thinking, what a radiologist is doing is examining a four-dimensional space (X,Y,Z, voxel grayscale) for relevant patterns and deviance from those patterns (Essentially a subtractive algorithm).  A fifth dimension can be added by including changes over time (comparison to a previous similar study at some prior point in time).

Rapid real-time pattern recognition in five variables on large data sets.  Done successfully day-in and day-out visually by your local radiologist.

Initial evaluation of a complex data set can give you something like this multiple scatter plot which I don’t find too useful:

Now, this data set, to me with my orientation and training, becomes much more useful:

A cursory visual inspection yields a potential pattern, the orange circles, which to me suggests a possible model drawn in blue.  That curve looks parabolic, which suggests a polynomial linear model might be useful for describing that particular set of data, so we can model it like this and then run the dataset in R to prove or disprove our hypothesis.

So, what I’m suggesting here is that by visually presenting complex data in a format of up to five dimensions (three axes, X, Y,Z, a point with grayscale corresponding to a normalized value, and a fifth, comparative dimension) complex patterns can be visually discovered, potentially quickly and on a screening basis, and then appropriate models can be tested to discover if they hold water.  I’ll save the nuts and bolts of this for a later post, but when a large dataset is evaluated (like an EHR) dimension reduction operations can allow focusing down on fewer variables to put it into a more visualization-friendly dataset.

And I’m willing to bet even money that if an analyst becomes intimately familiar with the dataset and visualization, as they spend more time with it and understand it better, they will be able to pick out relationships that will be absolutely mind-blowing.

Processes and Modeling – a quick observation

Is it not somewhat obvious to the folks reading this blog that this:

Is the same thing as this:

While I might be skewered for oversimplifying the process (and it is oversimplified – greatly), the fundamental principles are the same.  LOS for those not inured in the definition is Length of Stay, also known as Turn around Time (former is usually in days, latter in minutes or hours)

Out of curiosity, is anyone reading this blog willing to admit they are using something similar, or have tried to use something similar and failed?  I would love to know people’s thoughts on this.