What branches of mathematics do I need to know to make AI algorithms?

In summary, the conversation discusses the use of mathematics in artificial intelligence, specifically in algorithms that can allow a program to distinguish objects in pictures and make decisions based on data. The speaker suggests that while there is currently no formalized mathematical approach to AI, a background in discrete math, linear algebra, prob/stat, and possibly graph theory, is useful in different areas of AI. They also mention the importance of optimization algorithms and techniques such as neural networks, Kalman filters, and optimal control theory in AI.
  • #1
petormojer
15
0
I am in high school and I don't know much math.
By AI I mean Artificial Intelligence.

And by AI algorithms, I mean like algorithms that can allow a program to distinguish object from object in a picture, what key word to use based on data from the past, "learns" you and other objects, and etc.
 
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  • #2
I also responded to your other thread. In principle, computer science and mathematics are the same; if you can find a solution to a problem in one, you can do so for the other. But there is a big disconnect, in that mathematics does not (yet) deal with the mechanics of computational requirements, and the most efficient way to calculate functions.

From what I know, there is no formalized "mathy" way of expressing the algorithms used in artificial intelligence (and in computer science in general, really). I haven't seen a mathematical formalization of quicksort yet, anyway.

Combinatorics would come in handy, though. Really, you need to look at current vectors of attack to AI.

Take me with a grain of salt, though. I don't know about the high, arcane wizard math yet; I'm only up to differential equations, and my major is CS.
 
  • #3
petormojer said:
algorithms that can allow a program to distinguish object from object in a picture, what key word to use based on data from the past, "learns" you and other objects, and etc.
My first thought was neural networks (NN). You "train" a NN to recognize objects. This link seems to verify that NN is central to pattern recognition. http://www.dontveter.com/basisofai/basisofai.html
 
  • #4
The problem is that AI is a massive field. So, you're going to need vastly different kinds of math for different things within AI. From what I've heard, stuff like computer vision is very math-heavy. You can use partial differential equations and Fourier analysis and lots of stuff.

My general gut reaction is to say that you need to learn discrete math, linear algebra, and prob/stat. Maybe some basic graph theory. But that might depend on what you are trying to do. If you are trying to do game programming, I'm guessing you would need stuff that's covered in a more standard algorithms course, like shortest path algorithms and that sort of thing. For that, you just need some discrete math/graph theory. Part of the "math" is going to be in the subject itself, too.

But there is a big disconnect, in that mathematics does not (yet) deal with the mechanics of computational requirements, and the most efficient way to calculate functions.

That IS math. P = NP is one of the millennium problems, a set of 7 problems (6 left) that you can win a million dollars for solving. The only disconnect is the same disconnect that exists between theoretical computer science and practical programming. In practice, it might not only be about big O. You might have to time different algorithms to see which is that fastest on the type of input data that you have and so on, and you might care about constant factors and so on.
I haven't seen a mathematical formalization of quicksort yet, anyway.

The way I see it, quicksort IS just math. Sorting is closely related to permutations of finite, totally ordered sets. And I'm sure someone has written it out in full rigor somewhere. The fact that people don't normally bother to do that just means it's non-rigorous, rather than that it's not math. There is actual algebra and math involved in analyzing the running time (best case, worst case, average case), too, even in CS classes.
 
  • #5
... said:
But there is a big disconnect, in that mathematics does not (yet) deal with the mechanics of computational requirements, and the most efficient way to calculate functions.
I disagree. Many AI problems of pattern recognition boil down to optimizing the match of the observed image with the trained objects. There has been a lot of work on the mathematics of optimization algorithms. To see some of that, check out the Davidon-Fletcher-Powell algorithm, integer programming, neural networks, Kalman filters, fast Fourier transforms, and a variety of Operations Research techniques. See also optimal control theory.
 
  • #6
I think I should add multi-variable calculus to the list, since you need that to understand gradient descent and some of it for prob/stat.
 

1. What is the most important branch of mathematics for AI algorithms?

The most important branch of mathematics for AI algorithms is calculus. Calculus is used to optimize and make predictions in AI algorithms, making it an essential tool in building and training AI models.

2. Do I need to know statistics to make AI algorithms?

Yes, statistics is a crucial branch of mathematics for building AI algorithms. It is used to analyze and interpret data, make predictions, and evaluate the performance of AI models.

3. Are linear algebra skills necessary for creating AI algorithms?

Yes, linear algebra is an important branch of mathematics for AI algorithms. It is used to represent and manipulate data in matrices and vectors, which are essential for AI algorithms to process and learn from large datasets.

4. Is knowledge of discrete mathematics useful for AI algorithms?

Yes, discrete mathematics plays a significant role in AI algorithms. It is used to model decision-making processes, logic, and algorithms that are essential for building AI systems.

5. Do I need to have a deep understanding of mathematical concepts to make AI algorithms?

While a good understanding of mathematics is necessary for building AI algorithms, having a deep understanding of mathematical concepts may not be required. Many AI tools and libraries have made it easier to build AI models without extensive mathematical knowledge. Nonetheless, a basic understanding of key mathematical concepts is still important for creating successful AI algorithms.

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