Producing an accurate demand forecast has always been a challenge.

Most forecasting methods to date have largely been based on extrapolation techniques – ARIMA models being the most prevalent. These models rely on breaking down the time-series data into its main components: trend, seasonality and “noise” and then re-combining them back up at a future point in time. This technique is known as classical decomposition and is fine when a time-series can be broken down this way. And it can produce pretty accurate forecasts if the forecast user knows what they’re doing.

But what about a large grocery retailer who might have a series of complex promotional campaigns spread across the year? These campaigns might involve price reductions, multi-buys, loyalty points and percentage discounts amongst others and might also involve advertising on various promotional media (flyers, mailers, newspaper and TV ads to name but a few).

The standard statistical modeling processes cannot deal effectively with such a complex environment, resulting in companies having to employ large teams of expert forecasters just to get an idea of the expected demand of products over the next few weeks and months.

Even the large ERP vendors,  such as SAP and Oracle, and statistical software vendors, such as SAS, require experienced staff to operate their applications. These applications tend to rely on the traditional statistical techniques to produce their forecasts – requiring complex parameters to be defined as part of the modeling process.

Well, it seems there is a solution: Neural Networks.

NNs are parameter-less and self-configuring – all they need is the historic sales data. They’re primary use up until now has been as part of face recognition software, but there are seemingly endless uses for this technology. It also appears to be quite easy to implement – and no complex maths involved!

The beauty of neural networks is their ability to pick out patterns in data and identify relationships between different causal factors. This is perfect for modeling the complex behaviour of demand in relation to several simultaneous causal effects.

By further breaking down the problem say, using segmentation algorithms, and then creating a neural net for each segment it is possible to model ever more complex scenarios. Add to that a massively parallel, scalable architecture that allows forecasts to be generated in real-time and you’ve got the building blocks of a highly accurate forecasting system.

Video is one of the stimulating areas in electronic communications and multimedia applications. Video can do great things to enhance a presentation, illustration, or advertise a new product. Video files are photographic images played at speeds that make it appear to the human eyes as if its images or frames are in full motion. It does not wonder that the video files can be extremely large because the number of images required to give appearance of motion. A single second of uncompressed video running at 30 frames per second may require more than 30 Mega bytes of storage space.

The other challenge is how to deliver a video file over the internet with small storage and fast speed, eventhough the internet bandwith is low. In order to be used effetively, however, video is often compressed for storageand transfer, and then decompressed for use.

This research will find the meeting of two conflicting requirements, reducing the transmission bit-rate and increasing the image quality. Compression depends on two factors : (1) motion estimation – a process of estimating the pixels of the current frame from the reference frame, and (2) motion compensation – a process for the residual error after motion estimation. This research will develop a low bit-rate video coding system for video-telephone, video conferencing, and video streaming to mobile phones, which have limited processing and bandwith capacity.

The research goals are : Low bit-rate video coding algorithm focusing on moving region, apply error surface corelation in video coding, applying artificial neural network in presenting arbitrary shaped moving objects, and applying wavelet transformation algorithm to compress the video file and improve the quality of the iamges.

Applications of this research are studio-based and desktop video conferencing, surveillance and monitoring, telemedicine, computer based training, video phone, and video over internet.

Piedāvāju interesentiem savu pamatkodu neirālā tīkla implementācijai Java SE6,

package neuralnetwork;

public class NNx {

    public NNx() {
        w = new float[2];
        x = new float[4][2];
        s = new float[4][2];
        t = new float[4];

    }

    private void Initialization() {
        System.out.println("Giving input values");
        System.out.println("");
        //i integrated AND logical statement
        //i dont know why, but it didnt worked till i defined it for t[0],t[1],t[2],t[3]
        s[0][0] = 0;
        s[0][1] = 0;
        t[0] = -1;
        s[1][0] = 1;
        s[1][1] = 0;
        t[1] = -1;
        s[2][0] = 0;
        s[2][1] = 1;
        t[2] = -1;
        s[3][0] = 1;
        s[3][1] = 1;
        t[3] = 1;
        for (int i = 0; i < w.length; i++) {
            w[i] = (float)Math.random();
        }

        b = 1;
    }

    private void Training() {
        float sum = 0;

        for (int i = 0; i < x.length; i++) {
            for (int j = 0; j < x[i].length; j++) {
                x[i][j] = s[i][j];

            }

        }
        System.out.println("Network training in progress :");
        System.out.println("");

        for (iteration = 0; iteration < max_iteration; iteration++) {

            System.out.println("step " + (iteration + 1) + " done");
            for (int i = 0; i < x.length; i++) {

                sum = 0;
                for (int j = 0; j < x[i].length; j++) {
                    sum += x[i][j] * w[j];
                }
                y_in = b + sum;
                if (y_in >= threshold) {
                    y = 1;
                } else if (y_in < threshold) {
                    y = -1;
                }

                if (y != t[i]) {
                    for (int j = 0; j < w.length; j++) {
                        w[j] = w[j] + (learn_rate * t[i] * x[i][j]);
                    }
                    b = b + learn_rate * t[i];

                }
            }
        }
        System.out.println("");
        System.out.println("Solution has been found");
        System.out.println("");
    }

    private void Results() {
        float sum = 0;
        float[] res_output = new float[4];

        for (int i = 0; i < x.length; i++) {
            for (int j = 0; j < x[i].length; j++) {
                x[i][j] = s[i][j];
            }
        }

        System.out.println("Results : (for checking)");
        for (int i = 0; i < x.length; i++) {
            sum = 0;
            for (int j = 0; j < x[i].length; j++) {
                sum += x[i][j] * w[j];
            }
            y_in = b + sum;
            if (y_in >= threshold) {
                y = 1;
            } else if (y_in < threshold) {
                y = -1;
            }
            if (y == -1) {
                res_output[i] = 0;
            } else {
                res_output[i] = 1;
            }

        }
        System.out.println("");
        System.out.println("0 AND 0 = " + res_output[0]);
        System.out.println("0 AND 1 = " + res_output[1]);
        System.out.println("1 AND 0 = " + res_output[2]);
        System.out.println("1 AND 1 = " + res_output[3]);
    }

    public void RunPerceptron() {
        learn_rate = (float) 0.5;
        threshold = (float) 0.2;
        max_iteration = 10;
        Initialization();
        Training();
        Results();
    }

    public static void main(String[] args) {
        NNx perceptron = new NNx();
        perceptron.RunPerceptron();
    }
    private float[] w;
    private float b;
    private float[][] x;
    private float[][] s;
    private float y;
    private float learn_rate;
    private float threshold;
    private float[] t;
    private float y_in;
    private int iteration;
    private int max_iteration;
}

‘

Tātad tīkls atrisina elementāru AND funkciju izmantojot leraning algoritmu un single – layer elementus. PM ja ir kādi jautājumi, kodu var droši pārizmantot

In 13th century India,  the story was originally told of a group of blind men (or men in the dark) who touch an elephant to learn what it is like.  Each one touches a different part, but only one part, such as the side or the tusk.  They then compare notes on what they felt, and learn they are in complete disagreement.

With this ancient story in mind,  I’d like to introduce you to the annual conference of the Society for Neuroscience, or SfN, where brain enthusiasts across the globe gather for 5 days to compare notes – not on an elephant – but on something more massive – the brain and mind.  The vast complexities of neural development and communication will be shared amongst some 31,000+ participants in an effort to integrate findings from molecular to neural physiology to systems dynamics to behavior and find some  agreement on one of the all-time great biological mysteries.

As but a single humble molecular/cognitive/neuro/blogger, I will do my best to focus specifically on stories and highlights that address the dilemma of the bind men and the elephant and look for stories that  interlink different levels of analysis and help integrate data and models across different levels of analysis. I am fascinated by the way in which data from molecular levels of analysis can be interlinked with synaptic and systems levels of analysis and so hope to relate some of these interconnections with my readers.

You can readily follow the action at this years gathering using the fantastic organizational, informatic tools on the SfN meeting planner.  There are a number of resources to support neuro-bloggers and theme-specific neuro-tweeters.  Also, DrugMonkey has a growing list of other SfN tweeters/bloggers.  The real-time flow on Twitter #sfn09 as well as #sfnthemea & (b,c,d,e, and the notorious h) is already amazing !!

Please join the fray and share your thoughts with the SfN community! See you in Chicago.

Hello everyone,

though delayed (thanks to *indows), here comes my neuron model article. First of all, I want to make clear that none of these can be treated as a 100% truth. There may be mistakes everywhere…

Some bibliography

There is a very good intro to neural networks theory written by some other WordPress blogger. It can be found here.

There is also a great book in Polish, available on-line – by the master and pioneer of Neural Networks in Poland – prof. Tadeusiewicz, available here, which I wholeheartedly recommend.

About this source code

This is for those who want to learn how to create neural networks but never came across a simple example – for people like me. You get a lot of full-sized neural networks source code available on-line, whole C++ ANN libraries GPL-licensed, but never anything for a simple human being to start with. So I decided it was a high time to change that. From now on, I’ll keep posting NN-related source code, increasing its level of complicatedness. The examples will be based on the programs that come along with the book written by Tadeusiewicz. Those programs were written in QBASIC, which is rather ancient. So i’ll kind of port them to C++.

Source code itself…

can be found here. It’s not complete and idiot-proof so if you want to prove it’s not working, you can easily The idea is that you can characterize a flowe by two traits – it can smell good (or bad) and it can be colourfull. Those two traits can be assessed with a value ranging (for example) from -5 to 5. So you can teach the neuron to like flowers which smell very well (4-5) and are quite colourfull (2-3) and after few rounds (7 is usually enough) it can discern well those from the others and tell you how much it likes such flowers.. A pretty straightforward example but it should suffice to illustrate a simple neuron.

The neuron

is non-linear with activation function being f(x) = 1/(1 – exp(-x)). Its derivative is f(x)*(1-f(x)). Well, I guess you’ll get the rest from the source code. If not, comment and ask

Have fun,

dare2be

In previous posts, we have explored some of the basic molecular (de-repression of chromatin structure) and cellular (excess synaptogenesis) consequences of mutations in the MeCP2 gene – a.k.a the gene whose loss of function gives rise to Rett syndrome.  One of the more difficult aspects of understanding how a mutation in a lowly gene can give rise to changes in cognitive function is bridging a conceptual gap between biochemical functions of a gene product — to its effects on neural network structure and dynamics.  Sure, we can readily acknowledge that neural computations underlie our mental life and that these neurons are simply cells that link-up in special ways – but just what is it about the “connecting up part” that goes wrong during developmental disorders?

In a recent paper entitled, “Intact Long-Term Potentiation but Reduced Connectivity between Neocortical Layer 5 Pyramidal Neurons in a Mouse Model of Rett Syndrome” [doi: 10.1523/jneurosci.1019-09.2009] Vardhan Dani and Sacha Nelson explore this question in great detail.  They address the question by directly measuring the strength of neural connections between pyramidal cells in the somatosensory cortex of healthy and MeCP2 mutant mice.  In earlier reports, MeCP2 neurons showed weaker neurotransmission and weaker plasticity (an ability to change the strength of interconnection – often estimated by a property known as “long term potentiation” (LTP – see video)).   In this paper, the authors examined the connectivity of cortical cells using an electrophysiological method known as patch clamp recording and found that early in development, the LTP induction was comparable in healthy and MeCP2 mutant animals, and even so once the animals were old enough to show cognitive symptoms.  During these early stages of development, there were also no differences between baseline neurotransmission between cortical cells in normal and MeCP2 mice.  Hmmm – no differences? Yes, during the early stages of development, there were no differences between genetic groups – however – once the team examined later stages of development (4 weeks of age) it was apparent that the MeCP2 animals had weaker amplitudes of cortical-cortical excitatory neurotransmission.  Closer comparisons of when the baseline and LTP deficits occurred, suggested that the LTP deficits are secondary to baseline strength of neurotransmission and connectivity in the developing cortex in MeCP2 animals.

So it seems that MeCP2 can alter the excitatory connection strength of cortical cells.  In the discussion of the paper, the authors point out the importance of a proper balance of inhibition and excitation (yin and yang, if you will) in the construction or “connecting up part” of neural networks.  Just as Rett syndrome may arise due to such a problem in the proper linking-up of cells – who use their excitatory and inhibitory connections to establish balanced feedback loops – so too may other developmental disorders such as autism, Down’s syndrome, fragile X-linked mental retardation arise from an improper balance of inhibition and excitation.

pointer to: Computational Models of Basal Ganglia Function where Kenji Doya provides computational explanations for neuromodulators and their role in reinforcement learning. In his words, “Dopamine encodes the temporal difference error — the reward learning signal. Acetylcholine affects learning rate through memory updates of actions and rewards. Noradrenaline controls width or randomness of exploration. Serotonin is implicated in “temporal discounting,” evaluating if a given action is worth the expected reward.”

This type of amazing research provides a pathway to better understand how genes contribute to how the brain “works” as a 3-dimensional biochemical computational machine.

The homunculus (argument) is a pesky problem in cognitive science – a little guy who might suddenly appear when you propose a mechanism for decision making, spontaneous action or forethought  etc. – and would take credit for the origination of the neural impulse.  While there are many mechanistic models of decision making that have slain the little bugger – by invoking competition between past experience and memory as the source of new thoughts and ideas – one must always tread lightly, I suppose, to be wary that cognitive mechanisms are based completely in neural properties devoid of a homuncular source.

Still, the human mind must begin somewhere.  After all, its just a ball of cells initially, and then a tube and then some more folds, layers, neurogenesis and neural migration  etc. before maturing – miraculously – into a child that one day looks at you and says, “momma” or “dada”.  How do these neural networks come into being?  Who or what guides their development toward that unforgettable, “momma (dada)” moment?  A somewhat homuncluar “genetic program” – whose instructions we can attribute to millions of years of natural selection?  Did early hominid babies say “momma (dada)?  Hmmm. Seems like we might be placing a lot of faith in the so-called “instructions” provided by the genome, but who am I to quibble.

On the other hand, you might find that the recent paper by Akhtar et al., “Histone Deacetylases 1 and 2 Form a Developmental Switch That Controls Excitatory Synapse Maturation and Function” [doi:10.1523/jneurosci.0097-09.2009] may change the way you think about cognitive development.  The team explores the function of two very important epigenetic regulators of gene expression – histone deacetylases 1,2 (HDAC1, HDAC2) on the functionality of synapses in early developing mice and mature animals.  By epigenetic, I refer to the role of these genes in regulating chromatin structure and not via direct, site-specific DNA binding.  The way the HDAC genes work is by de-acetylating – removing acetyl groups – thus removing a electrostatic repulsion of acetyl groups (negative charge) on histone proteins with the phosphate backbone of DNA (also a negative charge).  When the histone proteins carry such an acetyl group, they do NOT bind well to DNA (negative-negative charge repulsion) and the DNA molecule is more open and exposed to binding of transcription factors that activate gene expression.  Thus if one (as Akhtar do) turns off a de-acetylating HDAC gene, then the resulting animal has a genome that is more open and exposed to transcription factor binding and gene expression.  Less HDAC = more gene expression!

What were the effects on synaptic function?  To summarize, the team found that in early development (neonatal mouse hippocampal cells) cells where the HDAC1 or 2 genes were turned off (either through pharmacologic blockers or via partial deletion of the gene(s) via lentivirus introduction of Cre recombinase) had more synapses and more synaptic electrical activity than did hippocampal cells from control animals.  Keep in mind that the HDACs are located in the nucleus of the neuron and the synapses are far, far away.  Amazingly – they are under the control of an epigenetic regulator of gene expression;  hence, ahem, “epigenetic puppetmasters”.  In adult cells, the knockdown of HDACs did not show the same effects on synaptic formation and activity.  Rather the cells where HDAC2 was shut down showed less synaptic formation and activity (HDAC1 had no effect).  Again, it is amazing to see effects on synaptic function regulated at vast distances.  Neat!

The authors suggest that the epigenetic regulatory system of HDAC1 & 2 can serve to regulate the overall levels of synaptic formation during early cognitive development.  If I understand their comments in the discussion, this may be because, you don’t necessarily want to have too many active synapses during the formation of a neural network.   Might such networks might be prone to excitotoxic damage or perhaps to being locked-in to inefficient circuits?  The authors note that HDACs interact with MecP2, a gene associated with Rett Syndrome – a developmental disorder (in many ways similar to autism) where neural networks underlying cognitive development in children fail to progress to support higher, more flexible forms of cognition.  Surely the results of Akhtar et al., must be a key to understanding and treating these disorders.

Interestingly, here, the controller of these developmental phenotypes is not a “genetic program” but rather an epigenetic one, whose effects are wide-spread across the genome and heavily influenced by the environment.  So no need for an homunculus here.

First, a disclaimer: I’m not a neuroscientist and do not wish to present myself as such. I have bachelor’s and master’s degrees in mathematics, and I work in heaalth information technology (HIT) as a senior software engineer. I would have loved to pursue a Ph.D. and work as a research scientist, but like so many other Americans, I had to make choices, and chose the “safe path”, working at a job that didn’t mean running the risk of not being able to obtain health insurance through my employer. We all know about the significant cost to employers, and the drain on our economy, of providing healthcare insurance. It may no be comfortably off the federal budget, but the cost to all of us in reduced wages, and the drag on our economy is still very real. The supposed lower costs to ordinary people of employer based healthcare are really illusory. But I digress.

The public debate over healthcare reform is surely very strange, and surprising. I don’t think the Obama administration anticipated the furor we are seeing, nor do I think many in congress did. It’s possible, of course, but that’s not really the point. The point is that people are now regularly saying and doing things that would have been inconceivable only a few years ago. I addressed this in an  earlier blog post Someone Started to Run. Today, I would like to revisit the same “tipping point” phenomenon, but from a different point of view. Instead of looking at the probability that people will adopt a particular behavior under a particular set of circumstances (essentially, a social psychological perspective), I propose a more self-consciously neurobiological approach. I say self-consciously because, in many ways, the underlying mathematics is similar, and I do not happen to think this is a coincidence.

For our purposes, there is no need to go into great detail about the neurobiology of learning except to note that strong associations between neurons (think of them as circuits that are closed, or easily closed) can be created that persist over time. This is called long-term potentiation (LPT). New memories are formed by creating or strengthening these associations. (Interestingly, implicit memories, such as the ability to juggle work a little differently). I will also note that one memory (whatever that is) does not equal one link, or synapse. It is a complex thing that corresponds to many interrelated associations. Think back to a particular event or occasion in your life, and you will likely become aware of a whole cascade of sounds, smells, words, maybe people, even forgotten disagreements or happy times together. It is as if though there is a whole sea of associations, no one of which takes you quickly to the particular event you are thinking about, but when you bring them all together it does. It’s a bit like painting a picture. There are colors, shades, shapes, that combine in certain ways, and it’s the way they fit together that matters.

Why does this matter? Well, aside from being interesting for its own sake, it helps to bridge the gap between the complexity of actual people or animals, and a simple model we’re about to consider. This model of learning is due to Donald  O. Hebb (1904-1985), and is usually known as “Hebbian learning”. We consider only networks of idealized neurons and links between them known as synapses. The only thing we need to know about a synapse in this simplified model is its strength (a number), and the only thing we need to know about the neuron is another number known as its threshold. Going back to real neurons for a moment, it is important to understand that at certain times they may “fire” an electric discharge to other neurons whose dendrites meet the axon of that neuron in what is called a (real) synapse. Chemical processes we won’t go into here (but this is where neurotransmitters enter the picture, if you’re curious) create a differential of positively and negatively charged ions across the synaptic cleft, and the potential difference becomes an electrical input to the neuron. But there are many, many neurons with axons terminating in the dendritic tree of the given neuron. I suppose it’s required to say that they don’t actually touch, but are separated by a synaptic cleft! All of these various dendrites can then “charge” the neuron a little bit. Well, okay, another seemingly irrelevant detail: some are excitatory and some are inhibitory, but let’s return to the neuron.

Do you recall that the neuron has a threshold potential? Well, when all the inputs “add up” to a certain level (I put this in quotes because the combination law isn’t linear), namely the threshold, the neuron “fires” and an electric charge flows through the axon to other neurons, and they follow a rule a bit like this.

Well, that’s all a bit complicated. We can idealize the situations by introducing synaptic strengths that can vary over time. Hebb’s rule is that when neurons fire at the association with the pre- and post-synaptic neurons become stronger, but when they do not fire this link becomes weaker over time. This is commonly enunciated in the maxim: “Neurons that fire together wire together”.

Okay, okay, enough already! What does this have to do with anything real? Well, let’s think about the ideas, slogans, and assumptions that are tossed about as part of the healthcare debate. Some are reasonable, some are patently absurd, but they seem to follow common “clusters”. Some participants in the debate will tell you about how there has to be a public option and there can be no compromise on this. Others will tell you about “death panels”, or government takeover of healthcare. These slogans are repeated so often that we often don’t think that much about them, about what is being said. They are effectively memes, evoking whole complexes of thoughts and ideas.

But wait, isn’t repetition of a phrase, an image, or an association going to strengthen certain associations we make? Remember, neurons that fire together wire together? I claim that it does. As the debate becomes more polarized (an ironic term when you think of the electrical polarization of a neuron) we hear these slogans more and more often and, interestingly, people become less and less likely to engage in, much less be persuaded by, reasoned arguments. Whether or not to start running isn’t that much of a decision when 80% of the people around you are already running the same direction.

At initial state, some hydrocarbon reservoirs have zero percent water cut at initial water saturation (Swi). The water cut increases gradually until the economic limit of oil production is reached and the well is shut-in.  A thoroughly analysis of recovery from individual wells is required to determine whether the oil is still remain in the fluid path. Some formation has affinity to oil. At the initial state of the formation, the pressure is still high, which is capable of moving oil into wellbore. In depletion period, the pressure is not strong enough to drag oil which is stuck on the formation pores. In this period, a newly drilled well tends to have a low influx since even the water is plugged by the stuck oil.

Figure 1: Well Drainage Radius

Let’s assume we have a hypothetical well with properties of as in Figure 1.  The well had produced 137 MSTBO. The production rate vs. cumulative time is plotted on log-log type-curve paper. The matched points are retrieved from the type curve and drainage radius is obtained which is 6200 ft. The volume of oil influenced by the well is 30 MMSTBO. The recovery is only 3%. The core from the well is saturated with formation fluid and imbibed by formation water or brine. The oil recovery is only 3.9% or slightly higher than current recovery. The same core is then imbibed by several surfactants. One of the surfactants can recover 26% of oil. If the surfactant is applied in the field, we can expect the well producing another 7.663 MMSTBO. We can positively conclude that the well has a huge oil potential left in the fluid flow path.

In the present invention of William Weiss, several field applications are suggested since there are a large number of variables involved. From those field applications, we will get several set variables. Those sets of variables are then inputted into Neural Network which will correlate all variables. Fuzzy logic is used as analytical tool through out the Neural Network. The output will be used to forecast the production and to determine the surfactant usages.

I’ve diverged briefly from my work with aoAIm to explore artificial neural networks, or ANNs.  These computational structures have more direct applicability to my work in algorithmic composition.  Although I do not like the idea of ANNs taking the place of a goal-driven A.I. (and, to some extent, I don’t believe they’ll ever come close to an AI built with “knowledge” rather than abstraction), I must admit, they can produce some very interesting patterns.  If nothing else, they are of great interest mathematically and musically.

Below are some graphs generated by a simple ANN engine I wrote today that includes a relatively simple but powerful recurrent ANN algorithm.  The network had just one input and one output, corresponding to x and y, respectively.  I used anywhere between 5 and 100 neurons in the experiments, with anywhere from 25 to 1000 synapses connecting the neurons.  I programmed 9 basic neuron types, including linear, threshold, sinusoidal, exponential, switch (gate), invert, and others.

I was very impressed over with how some of these turned out.  I’ve never seen anything quite like many of these graphs!  Note that there is NO randomness in the networks, other than the configuration of the neurons and synapses.  In other words, the networks are randomly generated, but are not allowed to use randomness when responding to input.  The seemingly-random “noise” in some of the graphs is, as best as I can tell, due to trigonometric “leaks” that cause infinite recursions involving sinusoidal functions.  When one recurses with sinusoids (shifting the output slightly before recursing, as the network would most likely do by running it through more neurons), the output becomes unpredictable (noisy) very quickly.  But it is not actually random.  In theory, each of these graphs could be written explicitly as a function (making great use of the Heaviside function, of course).

“Using Neural Networks to Model the Behavior and Decisions of Gamblers, in Particular, Cyber-Gamblers.” by Victor K. Y. Chan.

A system is written that utilizes a back-propagation neural network to model Texas Holdem gamblers’ behavior, based on data collected from a cyber gambling website.

This article describes the use of neural networks and an empirical data sample of, inter alia, the amounts of bets laid and the winnings/losses made in successive games by a number of cyber-gamblers to longitudinally model gambler’s behavior and decisions as to such bet amounts and the temporal trajectory of winnings/losses. The data was collected by videoing Texas Holdem gamblers at a cyber-gambling website.

The full article is available on Scribd.

The above diagrams shows the structure utilized for one of the two neural networks developed for the paper. This one, dubbed “M1″, attempts to predict the bet amounts laid by each individual Texas Holdem gambler, based on winnings and losses in immediately preceding games, and the gambler’s current account balance.

Apparently, the ANN was generally speaking pretty successful, showing a mean magnitude of relative error on the order of 10^(-2). Two things caught my eye: 1) General betting trends were very well represented by the model, but short-lived (“high-frequency”, if you will) deviances in behavior were not.  The author notes that the same can be said of financial market models. 2) The same model was developed to predict six different gamblers — and achieved a high accuracy of prediction. What does this mean?  In the words of the author Victor Chan:

The influence of a gambler’s skills, strategies, and personality on his/her successive bet amounts is almost totally reflected by the pattern(s) of his/her winnings/losses in the several immediately preceding games and his/her gambling account balance.

Exclamation mark.

Article found on SciAm:  “Artificial Intelligence Predicts Gambling Behavior” via Mindhacks.

Welcome back!

As I said last time, my aim with this blog is to introduce and teach people about the wonderful world of mathematics, science and programming. I spent many a night thinking of what would be the perfect topic for my first post. Dynamical systems? Celestial mechanics? Game programming in Ruby? I figured that I still have to figure out a few things before I can do posts on those (I have to figure out how to get mathematical formulas from LaTeX into HTML. Still reading up on the latex2html app).

So I finally decided on a topic that everybody is interested in – Neural Networks – that would be the stepping stone into my world and is also a combination of most of the fields that I am interested in. It can also serve as a great divergence point for each of the fields (mathematics, science, programming). Anyway, let’s get down to it.

The human brain is the most powerful computational tool known to man, with the ability to do millions upon billions of computations per second. Artificial neural networks are way to emulate and model the brain’s way of doing computations and are based on the actual biological neural networks in our brains.

Neurons (also called “nodes”) are the basic processors in the brain. Neurons are connected to each other to form a neural network. The neuron receives input which is weighed and if successful activates the neuron, which in turn sends a electrical signal (as output) to another neuron or to some other part of the brain and/or body.

Somewhere in the 1950s or ’60s some mathematician tried to apply this process to computational problems and so the artificial neural network was born. The basic artificial neuron can be modelled as a nonlinear multi-input device with weighted interconnections (also called synaptic weights or strengths). The cell body (soma) is presented by a nonlinear limiting or threshold function.

The simplest ANN is a perceptron. I decided to implement the perceptron (emulating the logical AND-gate without a learning algorithm) in Ruby. The class looks as follows:

class Perceptron

  attr_accessor :weights, :threshold, :inputs

  def initialize( input_array = [], weight_array = [], threshold_val = 0 )
    @weights = weight_array
    @inputs = input_array
    @threshold = threshold_val
  end

  def calculate_output
    value = @inputs.zip(@weights).inject(0) { |sum, i| sum + i[0]*i[1] }
    value < @threshold ? false : true
  end

  def self.run( input_array = [] )
    p = Perceptron.new( input_array, [1,1], 2 )
    puts p.calculate_output
  end

end

The class takes input and calculates the output via the calculate_output method (seeing if the artificial neuron fires). It takes the inputs, weighs them and evaluates them against a chose threshold value. As an example, the following

Perceptron.run( [0,0] )
Perceptron.run( [0,1] )
Perceptron.run( [1,0] )
Perceptron.run( [1,1] )

would simulate the logical AND-gate. This is one of the simplest neural networks out there. From here on they progress to include learning algorithms (Hopfield and Kohonen networks) and include hidden layers. But those are topics for other future posts.

I hope you enjoyed this brief introduction to neural networks and your brief time in my domain. Until next time!

P.S.: Here are some other useful links about neural networks:

• Neural Networks in Ruby
• Wikipedia article on neural networks
• The Nonlinear Workbook by W.H. Steeb – this textbook was my introduction to neural networks during my undergrad studies.

A couple of posts ago I wrote about an interview with Yann Le Cun. I subsequently found this interesting note in Smith’s Neural Networks for Statistical Modeling:

Backpropagation is an example of multiple invention. David Parker (1982,1985) and Yann LeCun (1986) working independently of each other and of the Rumelhart group, published similar discoveries. But none of these workers made the first discovery of backpropagation. That honor goes, belatedly, to Paul Werbos, whose 1974 Harvard Ph.D. thesis, Beyond Regression, contains the earliest exposition of the techniques involved (Werbos 1974).

Werbos’ 1974 discovery had gone unappreciated, but Rumelhart, Hinton, and Williams’ 1986 discovery did not. It kindled a firestorm of interest in Neural Networks.

I don’t know any details of Le Cun’s discovery in 1986, but I’m curious to look it up.  Note that it was published in the same year as the Rumelhart paper. Here’s the full reference:

Le Cun, Yann. 1986. Learning Processes in a Asymetric Threshold Network. In Disordered Systems and Biological Organization, ed. E. Bienenstock, F. Fogelman Soulie, and G. Weisbuch. Berlin: Springer.