We study data clustering problems with $\ell_p$-norm objectives (e.g.

Ho et. al (2024) attempts to estimate the degree of algorithmic progress from language models. They collect observational data on language models' loss and compute over time, and argue that as time has passed, language models' algorithmic efficiency has been rising. That is, the loss achieved for fixed compute has been dropping over time. In this note, I raise one potential methodological problem with the estimation strategy. Intuitively, if part of algorithmic quality is latent, and compute choices are endogenous to algorithmic quality, then resulting estimates of algorithmic quality will be contaminated by selection bias.

We study data clustering problems with \ell_p -norm objectives (e.g. The dataset consists of n points, and we want to find k centers such that (a) the objective is minimized, while (b) respecting the individual fairness constraint that every point v has a center within a distance at most r(v), where r(v) is v's distance to its (n/k) th nearest point. Jung, Kannan, and Lutz [FORC 2020] introduced this concept and designed a clustering algorithm with provable (approximate) fairness and objective guarantees for the \ell_\infty or \textsc{ k -Center} objective. Empirically, their algorithms outperform Jung et. In this paper, our main contribution is to use Linear Programming (LP) techniques to obtain better algorithms for this problem, both in theory and in practice.

Developing faster algorithms is an important but elusive goal for data scientists. The ability to accelerate complex computing tasks and reduce latency has far-reaching ramifications in areas such as natural language processing, video streaming, autonomous robotics, gaming, and extended reality. Yet for all the hype surrounding computer algorithms and the increasingly sophisticated ways they operate, a basic fact stands out: these algorithms are typically built atop matrix multiplication, a basic type of linear algebra. The underlying mathematical framework has not changed a great deal since the inception of computing--and finding more efficient formulas has proved elusive. It is an issue attracting growing attention--particularly as machine learning (ML), deep learning (DL), artificial intelligence (AI), and machine automation advance into the mainstream.

Non-parametric tests can determine the better of two stochastic optimization algorithms when benchmarking results are ordinal, like the final fitness values of multiple trials. For many benchmarks, however, a trial can also terminate once it reaches a pre-specified target value. When only some trials reach the target value, two variables characterize a trial's outcome: the time it takes to reach the target value (or not) and its final fitness value. This paper describes a simple way to impose linear order on this two-variable trial data set so that traditional non-parametric methods can determine the better algorithm when neither dominates. We illustrate the method with the Mann-Whitney U-test. A simulation demonstrates that U-scores are much more effective than dominance when tasked with identifying the better of two algorithms. We test U-scores by having them determine the winners of the CEC 2022 Special Session and Competition on Real-Parameter Numerical Optimization.

Classifying things comes quite natural to us: our books, movies and music all have genres; the things we study are split between different subjects and even the food we eat belongs to different cuisines! In recent years we've been able to develop better and better algorithms to classify text: models like BERT-ITPT-FiT (BERT withIn-Task Pre-Training Fine-Tuning) or XL-NET seem to be reigning champions in this category, at least in the 29 benchmark datasets available on PapersWithCode. In recent years we've been able to develop better and better algorithms to classify text: models like BERT-ITPT-FiT (BERT withIn-Task Pre-Training Fine-Tuning) or XL-NET seem to be reigning champions in this category, at least in the 29 benchmark datasets available on PapersWithCode. But what if we don't know the available categories for the texts we want to analyze? Take for example a corpus of conversations or a collection of books or articles that all belong to different specializations within the same subject: labels aren't always as clear cut as spam / not spam, we may not have any idea of how many or what kind of labels to expect, or normal pre-trained classification methods wouldn't have the in-depth domain knowledge required not to classify them as all the same, while not enough material, time or computational power is available to fine-tune a Transformer model.

January 9, 2020 – Check out how two Washington University researchers' debate resulted in winning the Olin Award which "recognizes scholarly research that has timely, practical applications for complex business management problems". Dennis Zhang and Jake Feldman's research was focused on machine learning and customer choice modeling (respectively) to create a better algorithm for online shopping choices. In the end, they combined their approaches into a new mathematical model for presenting product choices to customers which resulted in 28% higher revenue per visit providing $22M marginal increase in a week's time for Chinese online retail giant Alibaba. Guess what, Alibaba adopted the new algorithm! Congratulations to Zhang and Feldman on your Olin Award and job well done!

If you start to look into machine learning and the math behind it, you will quickly notice that everything comes down to an optimization problem. Even the training of neural networks is basically just finding the optimal parameter configuration for a really high dimensional function. In this article, we will go through the steps of solving a simple Machine Learning problem step by step. We will see why and how it always comes down to an optimization problem, which parameters are optimized and how we compute the optimal value in the end. To start, let's have a look at a simple dataset (x1, x2): If you are lucky, one computer in the dataset had the exactly same age as your, but that's highly unlikely.

Fueled by improvements in speech recognition, machine learning, better algorithms, cloud processing, and more powerful computing devices, the quality of machine translations is improving. Learning another language has never been a simple proposition. It can take months of study to absorb the basics and years to become fluent. Of course, there's the added headache that learning a language doesn't help if a person encounters one of the world's other 7,000 or so languages. "There has always been a need for human translators and interpreters," says Andrew Ochoa, CEO of translation technology firm Waverly Labs.

I mentioned in my last article that Artificial Intelligence is a large field, to get to being a large field it must have been around for some time, which it has. The term Artificial Intelligence (AI) was coined in 1956 at the Dartmouth Conference (New Hampshire) by Stanford University Professor John McCarthy (although he was an assistant professor at Dartmouth at the time). You could argue that AI has deep roots in Formal Reasoning but that would open up a huge philosophical debate and would probably take significantly more space and time to write and read! So why now, if AI has been around for 70 years what has changed in the past few years that has propelled AI into the mainstream? The answer is that the perfect wave has hit, three things have come together to give us the adoption rates that we see.