# Questions tagged [learning-theory]

Questions about the design and analysis of machine learning algorithms.

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9 views

### What does “smooth control” here mean?

I came across the following statement in this pdf. This allows the learner to have smooth control over the bias-complexity tradeoff. What does "smooth control" here mean? How do you understand ...
25 views

### What are the basics of CS i should know,before I start my journey into machine learning

I am myself a non-cs graduate and would love to be a machine learning engineer. I have learned to code and know the basics of <...
15 views

### How do you interpret this learning curve? [closed]

Loss is MSE; orange is validation loss, blue training loss. The task is NN regression (18 inputs, 2 outputs), one layer 300 hidden units. Tuning the lr, mom, l2 regularization parameters this is the ...
36 views

### VC dimension of the class of polynomial classifiers of degree $n$

I came across this statement on page 85 of the book "understanding machine learning: from theory to algorithms" The general idea is as follows: Consider a binary classiﬁcation problem with the ...
18 views

### How can I understand the multi-class version of “shattering” intuitively? [closed]

I'm learning machine learning. VC dimension is a good way to measure the complexity of hypothesis class for binary classifier and has a very good intuitive explanation from shattering. When we ...
20 views

### Covering numbers to show that H is agnostically PAC-learnable

Suppose $X=[0,1]$ and $Y=[0,1]$, and we use the squared loss Let's define the hypothesis class $H = {h(x) = (x-a)^2 : a \in [0,1]}$. Question: How can covering numbers be used to show that this ...
39 views

### How do you prove the Natarajan's Lemma intuitively?

Let $H$ be a hypothesis class of multiclass predictors; namely, each $h\in H$ is a function from $X$ to $[k]$. Denote the Natarajan dimension of $H$ by $Ndim(H)$. Hope you can give me an intuitive ...
14 views

### Hypothesis space in AdaBoost or general Machine learning

I was curious about the following: in most learning algorithms, when an algorithm is said to learn a concept class $C$ then the algorithm outputs a function from the hypothesis space $H$ and often ...
46 views

### How can the VC-dimension of Turing machine be finite?

The VC-dimension of a hypothesis class $\mathcal{H}$ is defined to be the size of the maximal set $C$ such that $\mathcal{H}$ cannot shutter. This paper shows that the VC-dimension of the set of all ...
69 views

### Dana Angluin's L* algorithm - Hypothesis inconsistent

is it possible for the Dana Angluin's L* algorithm that a hypothesis is inconsistent? So assume we have a closded observation table for a regular language L. Now after creating the hypothesis we will ...
39 views

### Why is Agnostic PAC learnability a stronger criterion as compared to the PAC learnability?

I am trying to understand the mentioned question. According to me, it should be other way around as it is easier to find hypothesis which is approximately correct compared to the optimal hypothesis in ...
46 views

### Weighting function for Non Uniform Learning

Consider a hypothesis class $H = \cup_{n=1}^{\infty} H_n$, where for every $n\in N$, $H_n$ is finite. Find a weighting function $w : H ->[0, 1]$ such that $\sum_{h \in H} w(h) ≤ 1$ and so that for ...
24 views

### what does this phrase mean: “train a policy network”

I am familiar with the basics (and perhaps a substantial amount of basics) of imitation learning and reinforcement learning. In IL (imitation), we take demonstrations from an assumed expert, which we ...
12 views

### OR functions and SQ-Learning

Anyone can describe or give a reference which has a clear description and detailed proof of the SQ-Learning algorithm for the OR class of Boolean functions?
29 views

### Query complexity of exact learning and combinatorial parameter

When defining the query complexity of exact learning for a concept $c$ (considered as a function from $\{0,1\}^n \mapsto \{0,1\}$) in a concept class $\mathcal{C}$, we often come across the following ...
40 views

### What are good examples of computational theories for A.I. according to David Marr's Definition?

I was reading David Marr's "Artificial Intelligence-A Personal View" and he talks about "computational theory of AI" or what he laters labels as "Type 1" Theory. He provides the example of Chomsky's ...
238 views

### VC dimension of finite unions of one-sided intervals

What is the VC dimension of $k$ finite unions of one-sided intervals: If we take 3 one-sided intervals like $(-\infty, a_1]$, $(-\infty, a_2]$ and $(-\infty, a_3]$, I think union of these ...
35 views

### Does selecting the same arm has the same reward?

In multi-armed bandit problem, we have a set of $K$ arms. In each round $t$, a bandit selects an arm $k$ and receives a reward $r_{kt}$. The objective is to maximize the rewards after $T$ rounds. My ...
52 views

### Automatic learning/discovery of logics

Are there efforts to automatically discover new logics? Logics are simple structures - they have formal language, deduction rules, semantics and certain properties that are proved or discarded for ...
101 views

303 views

### any hope for a universal automatic parser?

Say you are a program, and you are given some source code but you don't know in what language, it can be C++/Java/Python/Lisp/... all you know is that it is highly structured and LR(1) parse-able, and ...
382 views

### The VC dimension when the samples are fixed

The VC dimension is usually used in the following way. There is a space of hypotheses. There is an unknown probability distribution. We sample some training-samples from this distribution. We find the ...
59 views

### In the learning theory version of Occam's razor, why can't I just declare whatever hypothesis I want to be “shortest”?

Occam's razor states that shorter explanations (formally speaking, hypotheses) are more likely to be correct. Indeed this can be formalized: for a hypothesis class $\mathcal H$ one may ascribe ...
115 views

### Is SRM necessary to prove that a countable union of agnostic PAC learnable classes is nonuniformly learnable?

The following I believe is a direct proof of this fact. If a learner is tasked to be $\epsilon$-competitive with a hypothesis $h \in \mathcal H_n$, where $\mathcal H_n$ is agnostic PAC learnable, it ...
43 views

### Is there a non-linear version of ICA?

"Independent Component Analysis" is this : someone is sampling a random vector $s \in \mathbb{R}^d$ such that all its components $s_i$ are mutually independent and $\mathbb{E}[s_i^4] < 3$ and the ...
122 views

### Why is it NP-hard to learn a disjunction of k variables as a disjunction of fewer than k log n variables?

I'm looking at the claim in An algorithmic theory of learning: Robust concepts and random projection by R. I. Arriaga and S. Vempala (2006): Further, it is NP-hard to learn a disjunction of k ...
291 views

### VC dimension of monotone disjunctions of length k over n variables?

There are of course $n \choose k$ monotone disjunctions which bounds the VC dimension at $\log_2 {n \choose k}$. I'm wondering if this is bound at $k \log_2 n$? (Possibly follows from combinatorial ...
916 views

### single agent vs multiple agent reinforcement learning

I am confused about 'single' vs 'multiple' agent reinforcement learning. Let's say that I have 1 hunter who I am training to hunt 1 static prey, so that only the hunter is moving around. This is ...
31 views

### Learning a small disjunction using an input distribution of our choice

I have a boolean function $f: \{0,1\}^n \to \{0,1\}$ that I know takes the form $$f(x_1,\dots,x_n) = x_{i_1} \lor x_{i_2} \lor \dots \lor x_{i_k}.$$ I don't know the values of $i_1,\dots,i_k$, but I ...
95 views

### Learning a small disjunction

I have a boolean function $f: \{0,1\}^n \to \{0,1\}$ that I know takes the form $$f(x_1,\dots,x_n) = x_{i_1} \lor x_{i_2} \lor \dots \lor x_{i_k},$$ but I don't know the values of $i_1,\dots,i_k$. ...
101 views

### A clarification on the taxonomy of Evolutionary Algorithms

A rather basic question but I am confused about the characterization of a certain local search method which I want to describe in the framework of EAs. In particular, consider an EA which in every ...
929 views

### PAC learning axis parallel rectangles

I am trying to understand the proof that the axis parallel rectangles are PAC learnable in the realizable case. This means that given $\epsilon, \delta$ with enough data we can find a function $h$ ...
874 views

### How do I continue learning programming, beyond the basics? [closed]

DISCLAIMER: I understand that I might not be posting in the right part of StackExchange, or this question might have been asked before (I haven't found it). If this offends anybody, I apologize. I'm ...
148 views

### Sample Complexity for Real-Valued PAC-Learnable Functions

Can anyone shed some light on how the VC Dimension affects the sample complexity bounds of infinite hypothesis classes with real-valued outputs in PAC learning, or how to calculate the sample ...
2k views

### How to implement the regret matching algorithm?

My question is the following: How to calculate the regret in practice? I am trying to implement the regret matching algorithm but I do not understand how to do it. First, I have $n$ players with the ...
379 views

### Training Error & Convergence to True Error

I Take some online class for Machine Learning. one of teacher say this sentence. if we have m data points, the training error converges to the true error as m → ∞. i thought, this sentence not ...
596 views

### Over-fitting Always Occurs?

i get stuck in one sentence in machine learning. i read tom Mitchel book on ML, and some other materials. if we have small training set, always over-fit can occurs? or is likely to occurs? i read ...
Assume two hypotheses classes $H_A\subset H_B$ defined over the same instance space $\delta$. Assume also $VC(H_A)=d$, does this mean $VC(H_B)\geq d$ ? where $VC$ is the VC dimension. We can use the ...