International Predicciones de ice-hockey tomorrow

Canadá vs Suecia

Canadá ha mostrado una excelente cohesión en su línea ofensiva, con jugadores como Connor McDavid liderando el ataque. Por otro lado, Suecia cuenta con una defensa sólida y experimentada, lo que podría complicar las cosas para los canadienses. La clave del partido podría estar en la capacidad de Suecia para neutralizar a los delanteros estrella de Canadá.

Rusia vs Finlandia

Rusia llega al partido con una gran efectividad en el power play, lo que podría ser decisivo si logran obtener ventajas numéricas. Finlandia, por su parte, tiene uno de los porteros más formidables del torneo, lo que podría ser un factor determinante en la contienda.

Estados Unidos vs República Checa

Estados Unidos ha demostrado ser imparable en situaciones de alta presión, gracias a su juventud y talento emergente. La República Checa, sin embargo, tiene un juego más maduro y calculado, lo que podría sorprender a muchos si logran imponer su ritmo desde el inicio.

Tendencias Recientes

• Canadá: Ha ganado sus últimos cinco partidos consecutivos, mostrando una excelente forma ofensiva.
• Suecia: Ha tenido dificultades para marcar goles en sus últimos encuentros, lo que podría ser una preocupación ante el poderoso ataque canadiense.
• Rusia: Ha sido muy efectiva en situaciones especiales, especialmente en el power play.
• Finnland:: Su portero ha mantenido un promedio bajo de goles encajados en los últimos encuentros.
• Estados Unidos:: Ha mostrado una gran capacidad para remontar partidos cuando están abajo en el marcador.
• República Checa:: Ha mantenido un estilo de juego conservador pero efectivo.

Estatísticas Clave

• Promedio de Goles por Partido:
• Canadá: 4.2
• Suecia: 2.8
• Rusia: 3.5
• Finnland: 2.1
• Estados Unidos: 3.8
• República Checa: 2.9
• Efectividad del Power Play (%):
• Canadá: 25%
• Suecia: 18%
• Rusia: 30%
• Finnland: 20%
• Estados Unidos: 22%
• República Checa: 19%
• Efectividad del Penalty Kill (%):
• Canadá: 85%
• Suecia: 80%
• Rusia: 78%
• Finnland: 82%
• Estados Unidos: 84%
• República Checa: 81%

Cada uno de estos números ofrece una visión valiosa sobre las capacidades actuales de los equipos y puede influir significativamente en el resultado final del partido.

Jugadores Ofensivos Destacados

• Nathan MacKinnon (Canadá): Considerado uno de los mejores centrocampistas del mundo, MacKinnon es conocido por su velocidad y habilidad para crear oportunidades tanto para él como para sus compañeros.ankitshah32/ankitshah32.github.io<|file_sep|>/_posts/2018-09-26-why-pytorch.md --- layout: post title: "Why PyTorch" description: headline: modified: category: tags: imagefeature: mathjax: chart: comments: featured: --- * TOC {:toc} I have been working with PyTorch for almost a year now and I have been quite happy with it. Before that I worked with TensorFlow and I must say I am not missing it. The reason I like PyTorch over TensorFlow is that the two are fundamentally different in their approach to deep learning and hence the workflow is quite different. In this post I will try to explain why I prefer PyTorch over TensorFlow. ## The Functional Approach PyTorch is based on the functional programming paradigm and it uses functions as first class citizens. If you are familiar with the functional programming paradigm you know what this means. If you are not familiar with functional programming then here's an example. ### Example Let's start by writing a function to calculate the sum of two numbers. python def sum(x,y): return x + y Now let's use this function to calculate the sum of two numbers. python sum(1,2) # returns :3 We can also pass this function as an argument to another function. python def add_one(f): return f(1) add_one(sum) # returns :2 The above example shows how functions can be used as first class citizens. This approach is used extensively in PyTorch. Now let's see how it is done in PyTorch. ### Autograd in PyTorch Autograd is one of the core features of PyTorch. It allows you to calculate derivatives automatically using backpropagation. To use autograd we have to create variables that require gradients. python import torch # Create two tensors with requires_grad = True x = torch.tensor(1.,requires_grad=True) y = torch.tensor(2.,requires_grad=True) # Define a function f = lambda x,y:x**2 + x*y + y**2 # Calculate z=f(x,y) z = f(x,y) # Calculate gradients z.backward() # Print gradients print(x.grad,y.grad) The above example calculates gradients of the function `f` with respect to `x` and `y`. This is just an example but in practice we will define neural networks and optimize them using autograd. PyTorch provides some predefined layers that we can use or we can also define our own layers if needed. ### Defining Layers in PyTorch Defining layers in PyTorch is very easy. For example let's define a linear layer from scratch without using any pre-defined layers in PyTorch. This is just for illustration purposes so we won't be optimizing for speed or anything like that. python class LinearLayer(torch.nn.Module): def __init__(self,input_size,output_size): super(LinearLayer,self).__init__() self.weights = torch.nn.Parameter(torch.randn(input_size,output_size)) self.bias = torch.nn.Parameter(torch.randn(output_size)) def forward(self,x): return torch.matmul(x,self.weights) + self.bias input_size = output_size =5 layer = LinearLayer(input_size,output_size) x = torch.randn(10,input_size) out = layer(x) print(out.shape) # prints :torch.Size([10,5]) As you can see defining layers in PyTorch is very simple and flexible. We can also easily stack multiple layers together by defining another class that contains these layers. python class MLP(torch.nn.Module): def __init__(self,input_size,output_size,num_hidden_layers=1,num_hidden_units=5): super(MLP,self).__init__() self.layers = torch.nn.ModuleList() self.layers.append(LinearLayer(input_size,num_hidden_units)) for i in range(num_hidden_layers -1): self.layers.append(LinearLayer(num_hidden_units,num_hidden_units)) self.layers.append(LinearLayer(num_hidden_units,output_size)) def forward(self,x): for layer in self.layers[:-1]: x = layer(x) x = torch.relu(x) return self.layers[-1](x) input_size = output_size =5 mlp = MLP(input_size,output_size,num_hidden_layers=3,num_hidden_units=10) x = torch.randn(10,input_size) out = mlp(x) print(out.shape) # prints :torch.Size([10,5]) ## Why Functional Programming? So far we have seen how functional programming paradigm can be used in deep learning but why should we prefer it over the object oriented paradigm? Let's compare the two approaches by looking at an example from TensorFlow and then rewrite it using PyTorch. ### Example Let's take the example of logistic regression where we want to classify points on a plane into two classes. We will first train our model on some randomly generated data and then test it on some test data. We will implement logistic regression using both TensorFlow and PyTorch. #### Logistic Regression using TensorFlow Let's start by implementing logistic regression using TensorFlow. python import tensorflow as tf tf.set_random_seed(0) np.random.seed(0) # Generate random data points for training N,D=1000,2 X_train=np.random.randn(N,D) Y_train=(np.sum(X_train,axis=1)>0).astype(np.float32) # Generate random data points for testing N,D=5000,2 X_test=np.random.randn(N,D) Y_test=(np.sum(X_test,axis=1)>0).astype(np.float32) # Define placeholders for inputs and labels inputs=tf.placeholder(tf.float32,[None,D]) labels=tf.placeholder(tf.float32,[None]) # Define weights and bias for logistic regression model weights=tf.Variable(tf.random_normal([D])) bias=tf.Variable(tf.zeros([1])) # Define logistic regression model logits=tf.add(tf.matmul(inputs,tf.expand_dims(weights,-1)),bias) # Define loss function and optimizer loss=tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, labels=labels)) optimizer=tf.train.GradientDescentOptimizer(learning_rate=0.01).minimize(loss) # Initialize variables init=tf.global_variables_initializer() with tf.Session() as sess: sess.run(init) for i in range(1000): sess.run(optimizer,{inputs:X_train, labels:Y_train}) preds=sess.run(tf.round(tf.sigmoid(logits)),{inputs:X_test}) print("Accuracy:",np.mean(preds==Y_test)) The above code implements logistic regression using TensorFlow. It first generates some random data points for training and testing. Then it defines placeholders for inputs and labels. After that it defines weights and bias for logistic regression model. Then it defines logistic regression model using matrix multiplication and addition operations. Next it defines loss function and optimizer using sigmoid cross entropy loss function and gradient descent optimizer respectively. Finally it initializes all variables and runs the training loop for a specified number of iterations. After training it calculates predictions on test data and prints accuracy. #### Logistic Regression using PyTorch Now let's implement logistic regression using PyTorch. python import torch torch.manual_seed(0) # Generate random data points for training N,D=1000,2 X_train=torch.randn(N,D) Y_train=(torch.sum(X_train,dim=1)>0).float() # Generate random data points for testing N,D=5000,2 X_test=torch.randn(N,D) Y_test=(torch.sum(X_test,dim=1)>0).float() # Define weights and bias for logistic regression model weights=torch.nn.Parameter(torch.randn(D)) bias=torch.nn.Parameter(torch.zeros([1])) def forward(inputs): logits=torch.matmul(inputs.expand(-1,D),weights)+bias preds=torch.round(torch.sigmoid(logits)) return preds loss_func=torch.nn.BCEWithLogitsLoss() optimizer=torch.optim.SGD([weights,bias],lr=0.01,momentum=0.) for i in range(1000): preds=forward(X_train) loss=loss_func(preds,Y_train.unsqueeze(-1)) optimizer.zero_grad() loss.backward() optimizer.step() preds=forward(X_test) print("Accuracy:",torch.mean((preds==Y_test.unsqueeze(-1)).float())) The above code implements logistic regression using PyTorch. It first generates some random data points for training and testing. Then it defines weights and bias for logistic regression model as trainable parameters using `torch.nn.Parameter`. After that it defines forward pass of logistic regression model using matrix multiplication and addition operations followed by sigmoid activation function and rounding operation to get predictions as either `0` or `1`. Next it defines loss function using binary cross entropy with logits loss function provided by `torch.nn.BCEWithLogitsLoss`. Finally it initializes optimizer as stochastic gradient descent optimizer with specified learning rate and momentum values provided by `torch.optim.SGD`. Then it runs the training loop for specified number of iterations where at each iteration it calculates predictions on training data followed by calculating loss value followed by zeroing out gradients followed by backward pass to calculate gradients followed by updating parameters using optimizer step method. After training it calculates predictions on test data followed by calculating accuracy value which is printed at end of script execution. ## Conclusion In this post we have seen how functional programming paradigm can be used in deep learning by looking at examples from both TensorFlow and PyTorch frameworks. We have seen how defining layers in PyTorch is very simple and flexible due to its functional approach whereas defining layers in TensorFlow requires more boilerplate code due to its object oriented approach which makes code less readable especially when dealing with complex models having many layers such as convolutional neural networks or recurrent neural networks etc.<|file_sep|># ankitshah32.github.io<|file_sep|>* TOC {:toc} I am currently reading [Mathematics For Machine Learning](https://mml-book.github.io/book/mml-book.pdf). This post contains my notes on chapter "Numerical Linear Algebra". ## Eigenvalues And Eigenv