Teachers Keep on Teaching – ‘til I Reach my Highest Ground

Forgive me Stevie Wonder for slightly reordering your lyrics, but I think you’d agree that it’s hard to reach your highest ground without the help of teachers. Being a teacher is often a thankless job. Nobody gets rich or famous for being a teacher, yet the contribution teachers make to society is invaluable. So, in honor of Teacher Appreciation Week, I’d like to take the opportunity to thank some of the teachers who helped me reach my highest ground.

The Teachers Who Made Me What I Am Today

Erik Lawrence


My saxophone teacher from the age of 9 until I was 18, Erik is largely responsible for my love of music. Seeing that my career has largely centered around music and technology, Erik can largely take credit for planting the seed and nurturing the music branch of that tree. When I began to take an interest in the piano and composing Erik was quick to urge my parents to get me piano lessons. And when my parents wanted to buy me a new saxophone as a graduation present it was Erik who took me to the best New York area music stores to find the perfect sax. Beyond music, Erik was an extremely positive role model throughout my formative years. He taught me to treat others with respect, be accountable for my mistakes, and value my time and the time of others. For all of the above and much more I am grateful for the impact Erik had on my life.

David Snider


By the age of 13, I had taught myself to play piano, I was beginning to compose my own music, and I was slowly collecting a variety of audio electronics. I owned a Yamaha SY55 synthesizer with an onboard sequencer, a Tascam four-track recorder, and boxes of random audio cables. Recognizing my newfound passions Erik Lawrence convinced my parents to get me piano lessons and introduced me to David Snider. If Erik was my music guru then David was my technology guru. Upon realizing my knack for creating music and tinkering with anything music electronics-related, David managed to convince my parents to buy me my first computer (an Apple Mac) and my first audio software package (Mark of the Unicorn’s MOTU – Performer). He took my meandering teenage hobbies and turned them into a focused passion that would ultimately drive a large part of my career. David brought much more than technology to my life. He taught me how to play Jazz piano, something I still do to this day. In fact, 30+ years later I can still play the song Misty exactly the way he taught to me. While David may not remember this, he called me in the early days of my freshman year of Music school to wish me luck and give me some advice on avoiding some of the pitfalls of a musician’s life. It seemed inconsequential at the time but the fact that he cared enough to do that is remarkable.

Eileen M Curley

In the first quarter of my freshman year of high school, I had a failing grade in math. This was not acceptable in the Flaks household, so my mother reached out to the teacher to see if she had any advice on how I could improve my grade. Ms. Curley selflessly gave her own free time to provide me with extra help. It quickly became apparent that my problem with math was unrelated to my aptitude and purely a function of not paying attention and not doing the work. In no time at all, I went from an F to an A. That year I scored a 99 on New York State standardize math exam (the regents) losing only 1 point for carelessly not carrying a negative sign down to my final answer on one question. When Ms. Curley received the results from that exam, she took time out of her day to directly call my house and excitedly tell my Mother how well I did. My time with Ms. Curley was a turning point in my life. Little did she know that I would ultimately go on to be a math major in college, leading to a career in math and computer science.

William (Bill) Garbinsky (a.k.a. Mr. G)

William Garbinsky was a musician first and a high school music teacher second. He loved music and he gave innumerable hours during and after school to help students like me become better musicians. He taught the concert band, wind ensemble, marching band, and jazz band and I was a member of all of them. He gave band nerds like me a place to call home and surrounded us with a like-minded peer group that made us all feel like we were part of something bigger. Mr. G even took time out of his day to teach AP Music History and Music Theory classes to the small cohort of students who were interested. Thanks to those Advanced Placement College Credits I had some free time on my schedule when I entered a college, which I promptly filled with math classes. Sadly Mr. G passed away some years ago but I hope he knows what a difference he made in my life and the lives of countless others.

James (Jim) McElwaine


I was lucky enough to be accepted into the Conservatory of Music at Purchase College. I was even more fortunate to study under James McElwaine. Professor McElwaine was a Physics student before going full bore into music. So, when he stumbled upon a kid in his music program who was taking calculus classes as electives, he embraced it and pushed me to pursue it further. Beyond encouraging me to explore the math program, Jim recognized my passion for everything audio electronics related, and he opened every door he could, including getting me jobs running live sound for campus events, running the conservatories recording studios and he even got me my first real paid gig as a recording engineer. Professor McElwaine’s willingness to embrace and encourage my odd trajectory through music school played a huge role in my ability to progress into a master’s program that ultimately allowed me to go from using pro-audio equipment to building it.

Martin (Marty) Lewinter


If my music professor was a physicist then surely, I needed a math professor who was also a musician. Lucky for me the head of the math program Martin Lewinter also happened to be a seasoned musician. Professor Lewinter taught that very first calculus class I took as an elective. After witnessing my interest in math, Marty encouraged me to take on a second degree. Before long I was pursuing two simultaneous bachelor’s degrees with a focus in music composition and math/computer science. Professor Lewinter gave hours of his time towards helping me as the math curriculum progressively got harder and he continued to push me to excel in both the math and the music program. When I started applying to graduate schools with a heavier engineering focus, I picked up some textbooks to independently review. After struggling over some of the math equations I asked Professor Lewinter for some help. I still remember our conversation, where I showed him an equation in a book and he had to explain to me that engineers used j for imaginary numbers, not i, so as not to be confused with the variable for current. It was a simple thing that just might have prevented my first year in graduate school from turning into a complete disaster!

Ken Pohlmann


In my junior and senior years of college, I started to dive deeper into the underlying math behind the audio tools I was using. I happened to be reading a book called the Principles of Digital Audio and found a note about the author who was a professor of “music engineering” at the University of Miami. Music engineering sounded like an awfully good way to combine four grueling years of math and music education, so I sent Professor Pohlmann an email asking if he’d consider accepting a student without an undergraduate electrical engineering degree. Ken was kind enough to respond, and he recommended I take an extra year to get some basic engineering credits and he pointed me towards some textbooks that might give me an early head start. Well, I did buy the books, but I otherwise ignored him and applied to the program anyway. I still remember being overjoyed at receiving an acceptance letter where Ken told me that he thought my math background would carry me through the curriculum. With Professor Pohlmann and the University of Miami Music Engineering program, I stumbled into a small world of like-minded folks who had a passion for math and music. Professor Pohlman took a hodgepodge of academic pursuits I haphazardly pieced together and combined them into one coherent subject that would ultimately lead to my final career as an engineer, manager, and executive on countless audio projects.

Will Pirkle


How many teachers have fed you information that you can directly correlate to your current and future earnings? Not many, but that is exactly what Will Pirkle did for me and many others. Professor Pirkle was able to perfectly blend theory and practice and teach me how to effectively turn everything I had learned into real software that did amazing things with an audio signal. Will took all the ethereal subject matter I had learned over the years and made it into something I could feel and touch. It’s that skill set along with my own willingness to pester anybody for something I want, that led me to my first full-time job with a music software company called Opcode, (ironically a competitor of MOTU) bringing me full circle back to some of my earlier education. Will’s teaching has stood the test of time and I still find a use for some of what he taught. And whenever anybody asks for advice about the audio/music engineering space I regurgitate much of the knowledge Professor Pirkle imparted on me. Without a doubt, I can say that my employability and financial wellbeing are directly tied to everything I learned from Professor Pirkle.

To All the Teachers

While the eight teachers above had the most profound effect on my life there are many other teachers who contributed to my success and I’d like to offer my thanks to all of them. And to all the teachers out there who feel unappreciated, please remember that somewhere out there, in that sea of children, is a kid who just needs a little extra push to find out who they are and be the best version of themselves. Keep fighting for those kids because I am living proof of the impact you can have.

One Final Note of Gratitude

Since Mother’s Day is fast approaching, I’d be remiss if I didn’t thank the greatest teacher of them all, my Mother, Susan Flaks. My mother was there for every step of the journey described in this post. Whether that was teaching me my first notes on the piano, driving me to private music lessons, paying for that first computer, pushing me to get extra help when I needed it, paying for college, or just supporting me through my entire education, she was the root of all my academic and professional success. My mother was more than just an amazing parent, she was also a teacher for more decades than she would care for me to publicly comment on, and I know she had a positive influence on numerous students who like me, went on to be happy, healthy, and well-rounded adults, who have made a positive contribution to their communities and the world.

Voting is Just a Precision and Recall Optimization Problem

It’s hard to avoid the constant bickering about the results of our last election. Should mail-in voting be legal? Do we need stricter voter identification laws? Was there fraud in the last election? Did it impact the results? These are just a fraction of the questions circulating around elections and voter integrity these days. Sadly, these questions appear to be highly politicized and it’s unclear if anybody is really interested in asking what an optimal election system looks like.

In a true fair and accurate representative democracy, a vote not counted is just as costly as one inaccurately counted. More precisely, a single mother with no childcare who doesn’t vote because of 4-hour lines is just as damaging to the system as a vote for a republican candidate that is intentionally or accidentally recorded for the opposing Democratic candidate.

Therefore, we can conclude an optimal election system really involves optimizing on both axes. How do we make sure everyone who wants to vote gets to vote? And how do we ensure every vote is counted accurately? When viewed this way one can’t help but see the parallels to optimizing a machine learning classifier for precision (when we count votes for a given candidate how often did we get it right) and recall (of all possible votes for that candidate how many did we find).

Back the Truck Up! What is Precision and Recall Anyway

Precision and Recall are two metrics often used to measure the accuracy of a classifier. You might ask “why not just measure accuracy?” and that would be a valid question. Accuracy defined as everything we classified correctly divided by everything we evaluated, suffers from what is commonly known as the imbalanced class problem.

Suppose we have a classifier (a.k.a. laws and regulations) that can take a known set of voters who intend to vote “democrat” and “not democrat” (actual / input) and then outputs the recorded vote (predicted / output).

Let’s assume we evaluate 100 intended voters/votes, 97 of which intend to not vote for the democratic candidate and let’s build the dumbest classifier ever known. We are just going to count every vote as “not democrat”, regardless of whether the ballot was marked for the democratic candidate or not.

N (number of votes) = 100 Output (Predicted) Value
Democrat Not a Democrat
Input (Actual) Value Democrat TP = 0 FN = 3 TOTAL DEMOCRATS = 3
Not a Democrat FP = 0 TN = 97 TOTAL NOT DEMOCRATS = 97

To make our calculations a little easier we can take those numbers and drop them into a table that compares inputs to outputs also known as a confusion matrix. To simplify some of our future calculations we can further define some of the cells in the table above

  • True Positives (TP): Correctly captured an intended vote for the democrats as a vote for the democrats (97)
  • True Negatives (TN): Correctly captured a vote NOT intended for the democrats as a vote, not for the democrats (97)
  • False Positives (FP): Incorrectly captured a vote NOT intended for the democrats as a vote for the democrats (0)
  • False Negatives (FN): Incorrectly captured an intended vote for the democrats as a vote not for the democrats (3)

Now we can slightly relabel our accuracy equation and calculate our accuracy with our naïve classifier and the associated values from the table above.

97% Accuracy! We just created the world’s stupidest classifier and achieved 97% accuracy! And therein lies the rub. The second I expose this classifier to the real world with a more balanced set of inputs across classes we will quickly see our accuracy plummet. Hence, we need a better set of metrics. Ladies and gentlemen, I am delighted to introduce …

  • Precision: Of the votes recorded (predicted) for the Democrats, how many were correct

  • Recall: Of all possible votes for the Democrats, how many did we find

What becomes blatantly clear from evaluating these two metrics is that our classifier, which appeared to have great accuracy, is terrible. None of the intended votes for the democrats were correctly captured and of all possible intended votes for the democrats, we found none of them. It’s worth noting that the example I’ve presented here is for a binary classifier (democrat, not democrat) but these metrics can easily be adapted to multi-class systems that more accurately reflect our actual candidate choices in the United States.

There’s No Such Thing as 100% Precision and Recall

Gödel’s incompleteness theorem, which loosely states that every non-trivial formal system is either incomplete or inconsistent, likely applies to machine learning and artificial intelligence systems. In other words, since machine learning algorithms are built around our known formal mathematical systems there will be some truths they can never describe. A consequence of that belief and something I preach to everyone I work with is that there is really no such thing as 100% precision and recall. No matter how great your model is and what your test metrics tell you. There will always be edge cases.

So if 100% precision and recall is all but impossible what do we do? When developing products around machine learning classifiers, we often ask ourselves what is most important to the customer, precision, recall, or both. For example, if I create a facial recognition system that notifies the police if you are a wanted criminal, we probably want to air on the side of precision because arresting innocent individuals would be intolerable. But in other cases, like flagging inappropriate images on a social network for human review, we might want to air on the side of recall, so we capture most if not all images and allow humans to further refine the set.

It turns out that very often precision and recall can be traded off. Most classifiers emit a confidence score of sorts (also known as a SoftMax output) and by just varying the threshold on that output we can trade-off precision for recall and vice-vera. Another way to think about this is, if I require my classifier to be very confident in its output before I accept the result, I can tip the results in favor of precision. If I loosen my confidence threshold, I can tip it back in favor of recall.

And how might this apply in voting? Well, if I structure my laws and regulations such that every voter must vote in person with 6 forms of ID and the vote is tallied in front of the voter by a 10-person bipartisan evaluation team who must all agree … we will likely have very high precision. After all, we’ve greatly increased the confidence in the vote outcome. But at what expense? We will also likely slow down the voting process and create massive lines which will significantly increase the number of people who might have intended to vote but don’t actually do so, hence decreasing recall.

Remind me again what the hell this has to do with Voting

The conservative-leaning Heritage Foundation makes the following statement on their website:

“It is incumbent upon state governments to safeguard the electoral process and ensure that every voter’s right to cast a ballot is protected.”

I strongly subscribe to that statement and I believe it is critical to the success of any representative democracy. But ensuring that every voter’s right to cast a ballot is protected, requires not only that we accurately record the captured votes, but also ensure that every voter who intends to vote is unhindered in doing so.

Maybe we need to move entirely to in-person voting while simultaneously allocating sufficient funds for more polling stations, government-mandated paid time off, and government-provided childcare. Or maybe we need all mail-in ballots but some new process or technology to ensure the accuracy of the votes. Ultimately, I don’t pretend to know the right answer, or if we even have a problem, to begin with. What I do know is that if we wish to improve our election systems we must first start with data on where we stand today and then tweak our laws and regulations to simultaneously optimize for precision and recall.

So, the next time a politician proposes changes to our election system ask … no demand, they provide data on the current system and how their proposed changes will impact precision and recall. Because only when we optimize for both these metrics can we stop worrying about making America great again and start working on making America even greater!

Hello World!

I’m back!  After a long hiatus from blogging I’ve decided to give it a go again.  I’d like to use this blog as a forum for sharing my thoughts on advanced technologies like speech recognition, audio signal processing, natural language processing, and artificial intelligence.   Additionally I will be covering my theories on how to manage team’s building these types of technologies and how we bring these products to market.   I hope you find the content engaging and stay tuned for my first official post in the coming weeks!